For over three decades researchers have been studying the BDI modelof agency. Many robust multiagent systems have been developed, and a numberof BDI logics have been studied. Following this intensive development phase, theimportance of integrating BDI models with inconsistency handling and revisiontheory have been emphasized. There is also a demand for a tighter connectionbetween BDI-based implementations and BDI logics. In this paper, we addressthese postulates by introducing a novel, paraconsistent logical BDI model close toimplementation, with building blocks that can be represented as SQL/rule-baseddatabases. Importantly, tractability is achieved by reasoning as querying. Thisstands in a sharp contrast to the high complexity of BDI logics. We also extendbelief shadowing, a shallow and lightweight alternative to deep and computation-ally demanding belief revision, to encompass agents’ motivational attitudes.

Inheritance has intensively been studied in both object-oriented programming (Oop) and knowledge representation and reasoning (KRR). On the other hand, the approaches to multiple inheritance and related method resolution, developed in both domains, remain separated. The primary goal of this paper is to demonstrate how these approaches may be integrated using inheritance expressions. In particular, we examine inheritance as a belief bases management machinery designed to operate in dynamically changing environments where objects are embedded and act. We focus on objects that are belief bases containers, potentially participating in complex distributed reasoning scenarios. We show that inheritance expressions, inspired both by Oop and KRR, provide a simple yet flexible and powerful means for expressing inheritance and related belief/knowledge fusion.

Inheritance has intensively been investigated during the past decades in object-oriented programming and knowledge representation and reasoning areas. In the paper we focus on recently introduced inheritance expressions that allow one to represent dynamic concept hierarchies as well as fuse and disambiguate beliefs acquired by the objects involved. We focus on querying and reasoning about inheritance expressions using a four-valued paraconsistent formalism that has been developed over the last ten years. In particular, we show that querying inheritance expressions and formulas can be efficiently implemented. In addition, we provide tableaux for general reasoning purposes. Complexity of the investigated tools is also analyzed.

As a side-effect of the Covid-19 pandemic, significant decreases in medical procedures for noncommunicable diseases have been observed. This calls for a decision support assisting in the analysis of opportunities to relocate procedures among hospitals in an efficient or, preferably, optimal manner. In the current paper we formulate corresponding decision problems and develop linear (mixed integer) programming models for them. Since solving mixed integer programming problems is NP-complete, we verify experimentally their usefulness using real-world data about urological procedures. We show that even for large models, with millions of variables, the problems’ instances are solved in perfectly acceptable time.

The majority of contemporary software systems are developed using object-oriented tools and methodologies, where constructs like classes, inheritance and objects are first-class citizens. In the current paper we provide a novel formal framework for many-valued object-oriented inheritance in rule-based query languages. We also relate the framework to rough set-like approximate reasoning. Rough sets and their generalizations have intensively been studied and applied. However, the mainstream of the area mainly focuses on the context of information and decision tables. Therefore, approximations defined in the much richer object-oriented contexts generalize known approaches.

Belief shadowing is a relatively recent approach to belief change. In essence, shadowing depends on accepting beliefs of others at the expense of dismissing, perhaps temporarily, some of the own ones. As a transient belief change, it is useful when an agent, acting as a group member or playing a particular role, has to adopt adequate \"external\" beliefs. So far two forms of shadowing, single and multiple, have been considered. While the former specifies shadowing when an agent belongs to a single group or plays a single role, multiple shadowing relaxes this restriction.In the paper we generalize shadowing to arbitrary finitely many-valued logics and consider more complex semantical structures allowing arbitrarily nested sets of worlds. We show that in this general setting multiple shadowing can be represented by single shadowing. The complexity of queries involving such generic shadowing operators is also analyzed.

Recent work in the area of Knowledge Representation and Reasoning has focused on modification and optimization of knowledge bases (KB) through the use of forgetting operators of the form forget(KB, (R) over bar), where (R) over bar is a set of relations in the language signature used to specify the KB. The result of this operation is a new KB where the relations in (R) over bar are removed from the KB in a principled manner resulting in a more efficient representation of the KB for different purposes. The forgetting operator is also reflected semantically in terms of the relation between the original models of the KB and the models for the revised KB after forgetting. In this paper, we first develop a rough reasoning framework where our KBs consist of rough formulas with a semantics based on a generalization of Kleene algebras. Using intuitions from the classical case, we then define a forgetting operator that can be applied to rough KBs removing rough relations. A constructive basis for generating a new KB as the result of applying the forgetting operator to a rough KB is specified using second-order quantifier elimination techniques. We show the application of this technique with some practical examples.

The paper introduces ActLog, a rule-based language capable of specifying actions paraconsistently. ActLog is an extension of 4QL Bel \" role=\"presentation\"> Bel , a rule-based language for reasoning with paraconsistent and paracomplete belief bases and belief structures. Actions considered in the paper act on belief bases rather than states represented as sets of ground literals. Each belief base stores multiple world representations which can be though of as a representation of possible states. In this context ActLog’s action may be then seen as a method of transforming one belief base into another. In contrast to other approaches, ActLog permits to execute actions even if the underlying belief base state is partial or inconsistent. Finally, the framework introduced in this paper is tractable.

This paper introduces 4QL(Bel), a four-valued rule language designed for reasoning with paraconsistent and paracomplete belief bases as well as belief structures. Belief bases consist of finite sets of ground literals providing (partial and possibly inconsistent) complementary or alternative views of the world. As introduced earlier, belief structures consist of constituents, epistemic profiles and consequents. Constituents and consequents are belief bases playing different roles. Agents perceive the world forming their constituents, which are further transformed into consequents via the agents or groups epistemic profile. In order to construct 4QL(Bel), we extend 4QL, a four-valued rule language permitting for many forms of reasoning, including doxastic reasoning. Despite the expressiveness of 4QL(Bel), we show that its tractability is retained.

This paper is devoted to paraconsistent approximate reasoning with graded truth-values. In the previous research we introduced a family of many-valued logics parameterized by a variable number of truth/falsity grades together with a corresponding family of rule languages with tractable query evaluation. Such grades are shown here to be a natural qualitative counterpart of quantitative measures used in various forms of approximate reasoning. The developed methodology allows one to obtain a framework unifying heterogeneous reasoning techniques, providing also the logical machinery to resolve partial and incoherent information that may arise after unification. Finally, we show the introduced framework in action, emphasizing its expressiveness in handling heterogeneous approximate reasoning in realistic scenarios.

Classical Answer Set Programming is a widely known knowledge representation framework based on the logic programming paradigm that has been extensively studied in the past decades. Semantic theories for classical answer sets are implicitly three-valued in nature, yet with few exceptions, computing classical answer sets is based on translations into classical logic and the use of SAT solving techniques. In this paper, we introduce a variation of Kleene three-valued logic with strong connectives, R3\" role=\"presentation\">R3, and then provide a sound and complete proof procedure for R3\" role=\"presentation\">R3 based on the use of signed tableaux. We then define a restriction on the syntax of R3\" role=\"presentation\">R3 to characterize Kleene ASPs. Strongly-supported models, which are a subset of R3\" role=\"presentation\">R3 models are then defined to characterize the semantics of Kleene ASPs. A filtering technique on tableaux for R3\" role=\"presentation\">R3 is then introduced which provides a sound and complete tableau-based proof technique for Kleene ASPs. We then show a translation and semantic correspondence between Classical ASPs and Kleene ASPs, where answer sets for normal classical ASPs are equivalent to strongly-supported models. This implies that the proof technique introduced can be used for classical normal ASPs as well as Kleene ASPs. The relation between non-normal classical and Kleene ASPs is also considered.

In this extended abstract, we discuss the use of iteratively-supported formulas (ISFs) as a basis for computing strongly-supported models for Kleene Answer Set Programs (ASPK). ASPK programs have a syntax identical to classical ASP programs. The semantics of ASPK programs is based on the use of Kleene three-valued logic and strongly-supported models. For normal ASPK programs, their strongly supported models are identical to classical answer sets using stable model semantics. For disjunctive ASPK programs, the semantics weakens the minimality assumption resulting in a classical interpretation for disjunction. We use ISFs to characterize strongly-supported models and show that they are polynomially bounded.

Dealing with heterogeneous information sources and reasoning techniques allowing for incomplete and inconsistent information is one of current challenges in the area of knowledge representation and reasoning. We advocate for 4QL, a rule-based query language, as a proper tool allowing one to address these challenges. To justify this point of view we discuss a rescue robotics scenario for which a simulator has been developed and tested. In particular, we present a planner using 4QL and, therefore, capable to deal with lack of knowledge and inconsistencies. Through the case study we show that our approach allows one to use lightweight knowledge representation tools: due to the use of 4QL tractability of modeling and reasoning is guaranteed and high usability is achieved.

The current paper falls into a bigger research programme concerning construction of modern belief structures applicable in multiagent systems. In previous papers we approached individual and group beliefs via querying paraconsistent belief bases. This framework, covering deterministic belief structures, turned out to be tractable under some natural restrictions on implementation. Moreover, we have indicated a four-valued query language 4QL as an implementation tool guaranteeing tractability and capturing all PTime -constructible belief structures.In this paper we generalize our approach to the nondeterministic case. This is achieved by adjusting the key abstractions of epistemic profiles and belief structures to this new situation. Importantly, tractability of the approach is still maintained.

In contemporary autonomous systems, like robotics, the need to apply group knowledge has been growing consistently with the increasing complexity of applications, especially those involving teamwork. However, classical notions of common knowledge and common belief, as well as their weaker versions, are too complex. Also, when modeling real-world situations, lack of knowledge and inconsistency of information naturally appear. Therefore, we propose a shift in perspective from reasoning in multi-modal logics to querying paraconsistent knowledge bases. This opens the possibility for exploring a new approach to group beliefs. To demonstrate expressiveness of our approach, examples of social procedures leading to complex belief structures are constructed via the use of epistemic profiles. To achieve tractability without compromising the expressiveness, as an implementation tool we choose 4QL, a four-valued rule-based query language. This permits both to tame inconsistency in individual and group beliefs and to execute the social procedures in polynomial time. Therefore, a marked improvement in efficiency has been achieved over systems such as (dynamic) epistemic logics with common knowledge and ATL, for which problems like model checking and satisfiability are PSPACE- or even EXPTIME-hard.

It is known that the OWL 2RL Web Ontology Language Profile has PTime data complexity and can be translated into Datalog. However, the result of translation may consist of a Datalog program and a set of constraints in the form of negative clauses. Therefore, a knowledge base in OWL 2RL may be unsatisfiable. In the current paper we first identify a maximal fragment of OWL 2RL, called OWL 2RL+, with the property that every knowledge base expressed in OWL2RL+ can be translated to a Datalog program and hence is satisfiable. We then propose some extensions of OWL 2RL and OWL 2RL + that still have PTime data complexity. © 2014 Springer-Verlag Berlin Heidelberg.

Various generalizations of fuzzy reasoning are frequently used in decision making. While in many application areas it is natural to assume that truth degrees of a property and its complement sum up to 1, such an assumption appears problematic, e.g., in modeling ignorance. Therefore, in some generalizations of fuzzy sets, degrees of membership in a set and in its complement are separated and are no longer required to sum up to 1. In frequent cases, this separation of positive and negative evidences for concept membership is more natural. As we discuss in the current paper, symbolic explanations of results of such forms of reasoning provide additional important information. In the present paper we address two related questions: (i) given generalized fuzzy connectives and a finite set of truth values T, find a finitely-valued logic over T, explaining fuzzy reasoning, and (ii) given a finitely-valued logic, find a fuzzy semantics, explained by the given logic. We also show examples illustrating usefulness of the approach.

We study a Horn fragment called Horn-RegI of the regular description logic with inverse RegI, which extends the description logic ALC with inverse roles and regular role inclusion axioms characterized by finite automata. In contrast to the well-known Horn fragmentsEL, DL-Lite, DLP, Horn-SH IQ and Horn-SROIQof description logics, Horn-RegI allows a form of the concept constructor universal restriction to appear at the left hand side of terminological inclusion axioms, while still has PTIME data complexity. Namely, a universal restriction can be used in such places in conjunction with the corresponding existential restriction. We provide an algorithm with PTIME data complexity for checking satisfiability of Horn-RegI knowledge bases.

We introduce a Horn description logic called Horn-DL, which is strictly and essentially richer than Horn- SROIQ , while still has PTime data complexity. In comparison with Horn- SROIQ , HornDL additionally allows the universal role and assertions of the form irreflexive <em>(s)</em>, ¬s(a,b) , a≐̸b . More importantly, in contrast to all the well-known Horn fragments EL , DL-Lite, DLP, Horn- SHIQ , Horn- SROIQ of description logics, HornDL allows a form of the concept constructor “universal restriction” to appear at the left hand side of terminological inclusion axioms. Namely, a universal restriction can be used in such places in conjunction with the corresponding existential restriction. In the long version of this paper, we present the first algorithm with PTime data complexity for checking satisfiability of HornDL knowledge bases.

The logic TeamLog proposed by Dunin-Kęplicz and Verbrugge is used to express properties of agents’ cooperation in terms of individual, bilateral and collective informational and motivational attitudes like beliefs, goals and intentions. In this paper we isolate a Horn fragment of TeamLog, called Horn-TeamLog, and we show that it has PTime data complexity.

We study Horn fragments of serial multimodal logics which are characterized by regular grammars with converse. Such logics are useful for reasoning about epistemic states of multiagent systems as well as similarity-based approximate reasoning. We provide the first algorithm with PTIME data complexity for checking satisfiability of a Horn knowledge base in a serial regular grammar logic with converse.

Agents' beliefs can be incomplete and partially inconsistent. The process of agents' belief formation in such contexts has to be supported by suitable tools allowing one to express a variety of inconsistency resolving and nonmonotonic reasoning techniques.In this paper we discuss 4QL*, a general purpose rule-based query language allowing one to use rules with negation in the premises and in the conclusions of rules. It is based on a simple and intuitive semantics and provides uniform tools for lightweight versions of well-known forms of nonmonotonic reasoning. In addition, it is tractable w.r.t. data complexity and captures PTIME queries, so can be used in real-world applications.Reasoning in 4QL* is based on well-supported models. We simplify and at the same time generalize previous definitions of well-supported models and develop a new algorithm for computing such models.

This paper discusses an implementation of four speech acts: assert, concede, request and challenge in a paraconsistent framework. A natural four-valued model of interaction yields multiple new cognitive situations. They are analyzed in the context of communicative relations, which partially replace the concept of trust. These assumptions naturally lead to six types of situations, which often require performing conflict resolution and belief revision.The particular choice of a rule-based, DATALOG$^{\neg \neg}$-like query language 4QL as a four-valued implementation framework ensures that, in contrast to the standard two-valued approaches, tractability of the model is achieved.

The current paper is devoted to belief fusion when information sources may deliver incomplete and inconsistent information. In such cases paraconsistent and commonsense reasoning techniques can be used to complete missing knowledge and disambiguate inconsistencies. We propose a novel, realistic model of distributed belief fusion and an implementation framework guaranteeing its tractability.

We develop the first bisimulation-based method of concept learning, called BBCL, for knowledge bases in description logics (DLs). Our method is formulated for a large class of useful DLs, with well-known DLs like <em>ALC, SHIQ, SHOIQ, SROIQ</em>. As bisimulation is the notion for characterizing indis-cernibility of objects in DLs, our method is natural and very promising.

This book constitutes the refereed proceedings of the 6th KES International Conference on Agent and Multi-Agent Systems, KES-AMSTA 2012, held in Dubrovnik, Croatia, in June 2012. &lt;br&gt;The conference attracted a substantial number of researchers and practitioners from all over the world who submitted their papers for ten main tracks covering the methodology and applications of agent and multi-agent systems, one workshop (TRUMAS 2012) and five special sessions on specific topics within the field. The 66 revised papers presented were carefully reviewed and selected for inclusion in the book. The papers are organized in topical sections on virtual organizations, knowledge and learning agents, intelligent workflow, cloud computing and intelligent systems, self-organization, ICT-based alternative and augmentative communication, multi-agent systems, mental and holonic models, assessment methodologies in multi-agent and other paradigms, business processing agents, Trumas 2012 (first international workshop), conversational agents and agent teams, digital economy, and multi-agent systems in distributed environments.

Complex mission or task specification languages play a fundamentally important role in human/robotic interaction. In realistic scenarios such as emergency response, specifying temporal, resource and other constraints on a mission is an essential component due to the dynamic and contingent nature of the operational environments. It is also desirable that in addition to having a formal semantics, the language should be sufficiently expressive, pragmatic and abstract. The main goal of this paper is to propose a mission specification language that meets these requirements. It is based on extending both the syntax and semantics of a well-established formalism for reasoning about action and change, Temporal Action Logic (TAL), in order to represent temporal composite actions with constraints. Fixpoints are required to specify loops and recursion in the extended language. The results include a sound and complete proof theory for this extension. To ensure that the composite language constructs are adequately grounded in the pragmatic operation of robotic systems, Task Specification Trees (TSTs) and their mapping to these constructs are proposed. The expressive and pragmatic adequacy of this approach is demonstrated using an emergency response scenario.

In this paper we consider rule-based query languages with negation inbodies and heads of rules, traditionally denoted by DATALOG--. Tractable andat the same time intuitive semantics for DATALOG-- has not been provided evenif the area of deductive databases is over 30 years old. In this paper we identifysources of the problem and propose a query language, which we call 4QL.The 4QL language supports a modular and layered architecture and providesa tractable framework for many forms of rule-based reasoning both monotonicand nonmonotonic. As the underpinning principle we assume openness of theworld, which may lead to the lack of knowledge. Negation in rule heads may leadto inconsistencies. To reduce the unknown/inconsistent zones we introduce simpleconstructs which provide means for application-specific disambiguation ofinconsistent information, the use of Local Closed World Assumption (thus alsoClosed World Assumption, if needed), as well as various forms of default anddefeasible reasoning.

We develop a Web ontology rule language, called WORL, which combines a variant of OWL 2 RL with eDatalog-with-negation. We disallow the features of OWL 2 RL that play the role of constraints (i.e., the ones that are translated to negative clauses), but allow additional features like negation, the minimal number restriction and unary external checkable predicates to occur in the left hand side of concept inclusion axioms. Some restrictions are adopted to guarantee a translation into eDatalog-with-negation. We also develop the well-founded semantics for WORL and the standard semantics for stratified WORL (SWORL) via translation into eDatalog-with-negation. Both WORL and SWORL have PTime data complexity. In contrast to the existing combined formalisms, in WORL and SWORL negation in concept inclusion axioms is interpreted using nonmonotonic semantics.

A number of popular logical formalisms for representing and reasoning about the abilities of teams or coalitions of agents have been proposed beginning with the Coalition Logic (CL) of Pauly. Ågotnes et al introduced a means of succinctly expressing quantification over coalitions without compromising the computational complexity of model checking in CL by introducing Quantified Coalition Logic (QCL). QCL introduces a separate logical language for characterizing coalitions in the modal operators used in QCL. Boella et al, increased the representational expressibility of such formalisms by introducing Higher-Order Coalition Logic (HCL), a monadic second-order logic with special set grouping operators. Tractable fragments of HCL suitable for efficient model checking have yet to be identified. In this paper, we relax the monadic restriction used in HCL and restrict ourselves to the diamond operator. We show how formulas using the diamond operator are logically equivalent to second-order formulas. This permits us to isolate and define well-behaved expressive fragments of second-order logic amenable to model-checking in PTime. To do this, we appeal to techniques used in deductive databases and quantifier elimination. In addition, we take advantage of the monotonicity of the effectivity function resulting in exponentially more succinct representation of models. The net result is identification of highly expressible fragments of a generalized HCL where model checking can be done efficiently in PTime.

It is known that the OWL 2 RL Web Ontology Language Profile has PTime data complexity and can be translated into Datalog. However, a knowledge base in OWL 2 RL may be unsatisfiable. The reason is that, when translated into Datalog, the result may consist of a Datalog program and a set of constraints in the form of negative clauses. In this paper we first identify a maximal fragment of OWL 2 RL called OWL 2 RL⁺with the property that every knowledge base expressed in this fragment can be translated into a Datalog program and hence is satisfiable. We then propose some extensions of OWL 2 RL and OWL 2 RL⁺ that still have PTime data complexity.

The study of cooperation among agents is of central interest in multi-agent systems research. A popular way to model cooperation is through coalitional game theory. Much research in this area has had limited practical applicability as regards real-world multi-agent systems due to the fact that it assumes<em>deterministic</em> payoffs to coalitions and in addition does not apply to multi-agent environments that are<em>stochastic</em> in nature. In this paper, we propose a novel approach to modeling such scenarios where coalitional games will be contextualized through the use of logical expressions representing environmental and other state, and probability distributions will be placed on the space of contexts in order to model the stochastic nature of the scenarios. More formally, we present a formal representation language for representing contextualized coalitional games embedded in stochastic environments and we define and show how to compute <em>expected Shapley values</em> in such games in a computationally efficient manner. We present the value of the approach through an example involving robotics assistance in emergencies.

Description logics [1] refer to a family of formalisms concentrated around concepts, roles and individuals. They are used in many multiagent and semantic web applications as a foundation for specifying knowledge bases and reasoning about them. One of widely applied description logics is <em>SHIQ</em><img src=\"http://www.springerlink.com/jsMath/fonts/cmsy10/alpha/120/char53.png\" /><img src=\"http://www.springerlink.com/jsMath/fonts/cmsy10/alpha/120/char48.png\" /><img src=\"http://www.springerlink.com/jsMath/fonts/cmsy10/alpha/120/char49.png\" /><img src=\"http://www.springerlink.com/jsMath/fonts/cmsy10/alpha/120/char51.png\" /> [7,8]. In the current paper we address the problem of inconsistent knowledge. Inconsistencies may naturally appear in the considered application domains, for example as a result of fusing knowledge from distributed sources. We define three three-valued paraconsistent semantics for <em>SHIQ</em><img src=\"http://www.springerlink.com/jsMath/fonts/cmsy10/alpha/120/char53.png\" /><img src=\"http://www.springerlink.com/jsMath/fonts/cmsy10/alpha/120/char48.png\" /><img src=\"http://www.springerlink.com/jsMath/fonts/cmsy10/alpha/120/char49.png\" /><img src=\"http://www.springerlink.com/jsMath/fonts/cmsy10/alpha/120/char51.png\" />, reflecting different meanings of concept inclusion of practical importance. We also provide a quite general syntactic condition of safeness guaranteeing satisfiability of a knowledge base w.r.t. three-valued semantics and define a faithful translation of our formalism into a suitable version of a two-valued description logic. Such a translation allows one to use existing tools and <em>SHIQ</em><img src=\"http://www.springerlink.com/jsMath/fonts/cmsy10/alpha/120/char53.png\" /><img src=\"http://www.springerlink.com/jsMath/fonts/cmsy10/alpha/120/char48.png\" /><img src=\"http://www.springerlink.com/jsMath/fonts/cmsy10/alpha/120/char49.png\" /><img src=\"http://www.springerlink.com/jsMath/fonts/cmsy10/alpha/120/char51.png\" /> reasoners to deal with inconsistent knowledge.

There is a natural generalization of an indiscernibility relation used in rough set theory, where rather than partitioning the universe of discourse into indiscernibility classes, one can consider a covering of the universe by similarity-based neighborhoods with lower and upper approximations of relations defined via the neighborhoods. When taking this step, there is a need to tune approximate reasoning to the desired accuracy. We provide a framework for analyzing self-adaptive knowledge structures. We focus on studying the interaction between inputs and output concepts in approximate reasoning. The problems we address are: -given similarity relations modeling approximate concepts, what are similarity relations for the output concepts that guarantee correctness of reasoning? -assuming that output similarity relations lead to concepts which are not accurate enough, how can one tune input similarities?

In this paper we investigate a technique for fusing approximate knowledge obtained from distributed, heterogeneous information sources. We use a generalization of rough sets and relations [14], which depends on allowing arbitrary similarity relations. The starting point of this research is [2], where a framework for knowledge fusion in multi-agent systems is introduced. Agent’s individual perceptual capabilities are represented by similarity relations, further aggregated to express joint capabilities of teams. This aggregation, allowing a shift from individual to social level, has been formalized by means of dynamic logic. The approach of [2] uses the full propositional dynamic logic, not guaranteeing the tractability of reasoning. Therefore the results of [11, 12, 13] are adapted to provide a technical engine for tractable approximate database querying restricted to a Horn fragment of serial PDL. We also show that the obtained formalism is quite powerful in applications.

We give a novel tableau calculus and an optimal (EXPTIME) tableau decision procedure based on the calculus for the satisfiability problem of propositional dynamic logic with converse. Our decision procedure is formulated with global caching and can be implemented together with useful optimization techniques.

We give the first ExpTime (optimal) tableau decision procedure for checking satisfiability of a knowledge base in the description logic ALC, not based on transformation that encodes ABoxes by nominals or terminology axioms. Our procedure can be implemented as an extension of the highly optimized tableau prover TGC [12] to obtain an efficient program for the mentioned satisfiability problem.

We give a sound and complete tableau calculus for deciding the general satisfiability problem of regular grammar logics with converse (REG c logics). Tableaux of our calculus are defined as \"and-or\" graphs with global caching. Our calculus extends the tableau calculus for regular grammar logics given by Goré and Nguyen [11] by using a cut rule and existential automaton-modal operators to deal with converse. We use it to develop an ExpTime (optimal) tableau decision procedure for the general satisfiability problem of REG c logics. We also briefly discuss optimizations for the procedure.

The topic of preference modeling has recently attracted the interest of a number of sub-disciplines in artificial intelligence such as the nonmonotonic reasoning and action and change communities. The approach in these communities focuses on qualitative preferences and preference models which provide more natural representations from a~commonsense perspective. In this paper, we show how generalized circumscription can be used as a highly expressive framework for qualitative preference modeling. Generalized circumscription proposed by Lifschitz allows for predicates (and thus formulas) to be minimized relative to arbitrary pre-orders (reflexive and transitive). Although it has received little attention, we show how it may be used to model and reason about elaborate qualitative preference relations. One of the perceived weaknesses with any type of circumscription is the 2nd-order nature of the representation. The paper shows how a large variety of preference theories represented using generalized circumscription can in fact be reduced to logically equivalent first-order theories in a constructive way. Finally, we also show how preference relations represented using general circumscription can be extended with cardinality constraints and when these extensions can also be reduced to logically equivalent first-order theories.

Rough set approximations of Pawlak [15] are sometimes generalized by using similarities between objects rather than elementary sets. In practical applications, both knowledge about properties of objects and knowledge of similarity between objects can be incomplete and inconsistent. The aim of this paper is to define set approximations when all sets, and their approximations, as well as similarity relations are four-valued. A set is four-valued in the sense that its membership function can have one of the four logical values: unknown (<strong>u</strong>), false (<strong>f</strong>), inconsistent (<strong>i</strong>), or true (<strong>t</strong>). To this end, a new implication operator and set-theoretical operations on four-valued sets, such as set containment, are introduced. Several properties of lower and upper approximations of four-valued sets are also presented.

This paper presents a language for defining four-valued rough sets and to reason about them. Our framework brings together two major fields: rough sets and paraconsistent logic programming. On the one hand it provides a paraconsistent approach, based on four-valued rough sets, for integrating knowledge from different sources and reasoning in the presence of inconsistencies. On the other hand, it also caters for a specific type of uncertainty that originates from the fact that an agent may perceive different objects of the universe as being indiscernible. This paper extends the ideas presented in [9]. Our language allows the user to define similarity relations and use the approximations induced by them in the definition of other four-valued sets. A positive aspect is that it allows users to tune the level of uncertainty or the source of uncertainty that best suits applications.

This paper focuses on modelling perception and vague concepts in the context of multiagent Bgi (<em>Beliefs, Goals</em> and <em>Intentions</em>) systems. The starting point is the multimodal formalization of such systems. Then we make a shift from Kripke structures to similarity structures, allowing us to model perception and vagueness in an uniform way, “compatible” with the multimodal approach. As a result we introduce and discuss <em>approximate B</em> <em>gi</em> <em>systems</em>, which can also be viewed as a way to implement multimodal specifications of Bgi systems in the context of perception.

The multi-agent system paradigm has proven to be a useful means of abstraction when considering distributed systems with interacting components. It is often the case that each component may be viewed as an intelligent agent with specific and often limited perceptual capabilities. It is also the case that these agent components may be used as information sources and such sources may be aggregated to provide global information about particular states, situations or activities in the embedding environment. This paper investigates a framework for information fusion based on the use of generalizations of rough set theory and the use of dynamic logic as a basis for aggregating similarity relations among objects where the similarity relations represent individual agents perceptual capabilities or limitations. As an added benefit, it is shown how this idea may also be integrated into description logics.

In the current paper we first show that the fixpoint theory of equality is decidable. The motivation behind considering this theory is that second-order quantifier elimination techniques based on a theorem given in [16], when successful, often result in such formulas. This opens many applications, including automated theorem. proving, static verification of integrity constraints in databases as well as reasoning with weakest sufficient and strongest necessary conditions.

In the current paper we provide two methods for quantifier elimination applicable to a large class of formulas of the elementary set theory. The first one adapts the Ackermann method [1] and the second one adapts the fixpoint method of [20]. We show applications of the proposed techniques in the theory of correspondence between modal logics and elementary set theory. The proposed techniques can also be applied in an automated generation of proof rules based on the semantic-based translation of axioms of a given logic into the elementary set theory.

The relation of similarity is essential in understanding and developing frameworks for reasoning with vague and approximate concepts. There is a wide spectrum of choice as to what properties we associate with similarity and such choices determine the nature of vague and approximate concepts defined in terms of these relations. Additionally, robotic systems naturally have to deal with vague and approximate concepts due to the limitations in reasoning and sensor capabilities. Halpern [1] introduces the use of subjective and objective states in a modal logic formalizing vagueness and distinctions in transitivity when an agent reasons in the context of sensory and other limitations. He also relates these ideas to a solution to the Sorities and other paradoxes. In this paper, we generalize and apply the idea of similarity and tolerance spaces [2,3,4,5], a means of constructing approximate and vague concepts from such spaces and an explicit way to distinguish between an agent’s objective and subjective states. We also show how some of the intuitions from Halpern can be used with similarity spaces to formalize the above-mentioned Sorities and other paradoxes.

A general similarity-based algorithm for extracting ontologies from data has been provided in [1]. The algorithm works over arbitrary approximation spaces, modeling notions of similarity and mereological part-of relations (see, e.g., [2, 3, 4, 5]). In the current paper we propose a novel technique of machine learning similarity on tuples on the basis of similarities on attribute domains. The technique reflects intuitions behind tolerance spaces of [6] and similarity spaces of [7]. We illustrate the use of the technique in extracting ontologies from data.

Biochemical pathways or networks are generic representations used to model many different types of complex functional and physical interactions in biological systems. Models based on experimental results are often incomplete, e.g., reactions may be missing and only some products are observed. In such cases, one would like to reason about incomplete network representations and propose candidate hypotheses, which when represented as additional reactions, substrates, products, would complete the network and provide causal explanations for the existing observations. In this paper, we provide a logical model of biochemical pathways and show how abductive hypothesis generation may be used to provide additional information about incomplete pathways. Hypothesis generation is achieved using weakest and strongest necessary conditions which represent these incomplete biochemical pathways and explain observations about the functional and physical interactions being modeled. The techniques are demonstrated using metabolism and molecular synthesis examples.

We provide a logical model of biochemical reactions and show how hypothesis generation using weakest sufficient and strongest necessary conditions may be used to provide additional information in the context of an incomplete model of metabolic pathways.

In this paper, we propose a framework that provides software and robotic agents with the ability to ask approximate questions to each other in the context of heterogeneous and contextually limited perceptual capabilities. The framework focuses on situations where agents have varying ability to perceive their environments. These limitations on perceptual capability are formalized using the idea of tolerance spaces. It is assumed that each agent has one or more approximate databases where approximate relations are represented using intuitions from rough set theory. It is shown how sensory and other limitations can be taken into account when constructing approximate databases for each respective agent. Complex relations inherit the approximativeness inherent in the sensors and primitive relations used in their definitions. Agents then query these databases and receive answers through the filters of their perceptual limitations as represented by tolerance spaces and approximate queries. The techniques used are all tractable.

This paper focuses on the use and interpretation of approximate databases where both rough sets and indiscernibility partitions are generalized and replaced by approximate relations and similarity spaces. Similarity spaces are used to define neighborhoods around individuals and these in turn are used to define approximate sets and relations. There is a wide spectrum of choice as to what properties the similarity relation should have and how this affects the properties of approximate relations in the database. In order to make this interaction precise, we propose a technique which permits specification of both approximation and similarity constraints on approximate databases and automatic translation between them. This technique provides great insight into the relation between similarity and approximation and is similar to that used in modal correspondence theory. In order to automate the translations, quantifier elimination techniques are used.

In this paper, we propose a framework that provides software and robotic agents with the ability to ask approximate questions to each other in the context of heterogeneous ontologies and heterogeneous perceptive capabilities.The framework combines the use of logic-based techniques with ideas from approximate reasoning. Initial queries by an agent are transformed into approximate queries using weakest sufficient and strongest necessary conditions on the query and are interpreted as lower and upper approximations on the query. Once the base communication ability is provided, the framework is extended to situations where there is not only a mismatch between agent ontologies, but the agents have varying ability to perceive their environments. This will affect each agent’s ability to ask and interpret results of queries. Limitations on perceptive capability are formalized using the idea of tolerance spaces.

In the paper we present a purely logical approach to estimating computational complexity of potentially intractable problems. The approach is based on descriptive complexity and second-order quantifier elimination techniques. We illustrate the approach on the case of the transversal hypergraph problem, TRANSHYP, which has attracted a great deal of attention. The complexity of the problem remains unsolved for over twenty years. Given two hypergraphs, G and H, TRANSHYP depends on checking whether G = H-d, where H-d is the transversal hypergraph of H. In the paper we provide a logical characterization of minimal transversals of a given hypergraph and prove that checking whether G subset of or equal to H-d is tractable. For the opposite inclusion the Problem still remains open. However, we interpret the resulting quantifier sequences in terms of determinism and bounded nondeterminism. The results give better upper bounds than those known from the literature, e.g., in the case when hypergraph H, has a sub-logarithmic number of hyperedges and (for the deterministic case) all hyperedges have the cardinality bounded by a function sub-linear wrt maximum of sizes of G and H.

In traditional approaches to knowledge representation, notions such as tolerance measures on data, distance between objects or individuals, and similarity measures between primitive and complex data structures are rarely considered. There is often a need to use tolerance and similarity measures in processes of data and knowledge abstraction because many complex systems which have knowledge representation components such as robots or software agents receive and process data which is incomplete, noisy, approximative and uncertain. This paper presents a framework for recursively constructing arbitrarily complex knowledge structures which may be compared for similarity, distance and approximativeness. It integrates nicely with more traditional knowledge representation techniques and attempts to bridge a gap between approximate and crisp knowledge representation. It can be viewed in part as a generalization of approximate reasoning techniques used in rough set theory. The strategy that will be used is to define tolerance and distance measures on the value sets associated with attributes or primitive data domains associated with particular applications. These tolerance and distance measures will be induced through the different levels of data and knowledge abstraction in complex representational structures. Once the tolerance and similarity measures are in place, an important structuring generalization can be made where the idea of a tolerance space is introduced. Use of these ideas is exemplified using two application domains related to sensor modeling and communication between agents.

The premise of this paper is that the acquisition, aggregation, merging and use of information requires some new ideas, tools and techniques which can simplify the construction, analysis and use of what we call ephemeral knowledge structures. Ephemeral knowledge structures are used and constructed by granular agents. Each agent contains its own granular information structure and granular information structures of agents can be combined together. The main concept considered in this paper is an information granule. An information granule is a concise conceptual unit that can be integrated into a larger information infrastructure consisting of other information granules and dependencies between them. The novelty of this paper is that it provides a concise and formal definition of a particular view of information granule and its associated operators, as required in advanced knowledge representation applications.

Second-order quantifier elimination in the context of classical logic emerged as a powerful technique in many applications, including the correspondence theory, relational databases, deductive and knowledge databases, knowledge representation, commonsense reasoning and approximate reasoning. In the current paper we generalize the result of [19] by allowing modal operators. This allows us to provide a unifying framework for many applications, that require the use of intensional concepts. Examples of applications of the technique in AI are also provided.

Introduction: Logic engineering often involves the development of modeling tools and inference mechanisms (both standard and non-standard) which are targeted for use in practical applications where expressiveness in representation must be traded off for efficiency in use. Some representative examples of such applications would be the structuring and querying of knowledge on the semantic web, or the representation and querying of epistemic states used with softbots, robots or smart devices. In these application areas, declarative representations of knowledge enhance the functionality of such systems and also provide a basis for insuring the pragmatic properties of modularity and incremental composition. In addition, the mechanisms developed should be tractable, but at the same time, expressive enough to represent such aspects as default reasoning, or approximate or incomplete representations of the environments in which the entities in question are embedded or used, be they virtual or actual. [...]

A technique is proposed for computing the weakest sufficient (wsc) and strongest necessary (snc) conditions for formulas in an expressive fragment of first-order logic using quantifier elimination techniques. The efficacy of the approach is demonstrated by using the techniques to compute snc's and wsc's for use in agent communication applications, theory approximation and generation of abductive hypotheses. Additionally, we generalize recent results involving the generation of successor state axioms in the propositional situation calculus via snc's to the first-order case. Subsumption results for existing approaches to this problem and a re-interpretation of the concept of forgetting as a process of quantifier elimination are also provided.

We present a sound and complete, tractable inference method for reasoning with localized closed world assumptions (LCWA’s) which can be used in applications where a reasoning or planning agent can not assume complete information about planning or reasoning states. This <em>Open World Assumption</em> is generally necessary in most realistic robotics applications. The inference procedure subsumes that described in Etzioni et al [9], and others. In addition, it provides a great deal more expressivity, permitting limited use of negation and disjunction in the representation of LCWA’s, while still retaining tractability. The ap- proach is based on the use of circumscription and quantifier elimination techniques and inference is viewed as querying a deductive database. Both the preprocessing of the database using circumscription and quan- tifier elimination, and the inference method itself, have polynomial time and space complexity.

Recently, Haas, Schubert, and Reiter, have developed an alternative approach to the frame problem which is based on the idea of using <em>explanation closure axioms</em>. The claim is that there is a monotonic solution for characterizing nonchange in serial worlds with fully specified actions, where one can have both a succinct representation of frame axioms and an effective proof theory for the characterization. In the paper, we propose a circumscriptive version of explanation closure, PMON, that has an effective proof theory and works for both context dependent and nondeterministic actions. The approach retains representational succinctness and a large degree of elaboration tolerance, since the process of generating closure axioms is fully automated and is of no concern to the knowledge engineer. In addition, we argue that the monotonic/nonmonotonic dichotomy proposed by others is not as sharp as previously claimed and is not fully justified.

We first define general domain circumscription (GDC) and provide it with a semantics. GDC subsumes existing domain circumscription proposals in that it allows varying of arbitrary predicates, functions, or constants, to maximize the minimization of the domain of a theory We then show that for the class of semi-universal theories without function symbols, that the domain circumscription of such theories can be constructively reduced to logically equivalent first-order theories by using an extension of the DLS algorithm, previously proposed by the authors for reducing second-order formulas. We also isolate a class of domain circumscribed theories, such that any arbitrary second-order circumscription policy applied to these theories is guaranteed to be reducible to a logically equivalent first-order theory. In the case of semi-universal theories with functions and arbitrary theories which are not separated, we provide additional results, which although not guaranteed to provide reductions in all cases, do provide reductions in some cases. These results are based on the use of fixpoint reductions.