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High-level Mission Specification and Planning for Collaborative Unmanned Aircraft Systems using Delegation.
Unmanned Systems, ??(??):??–??. World Scientific.
Publication status: Accepted
Automated specification, generation and execution of high level missions involving one or more heterogeneous unmanned aircraft systems is in its infancy. Much previous effort has been focused on the development of air vehicle platforms themselves together with the avionics and sensor subsystems that implement basic navigational skills. In order to increase the degree of autonomy in such systems so they can successfully participate in more complex mission scenarios such as those considered in emergency rescue that also include ongoing interactions with human operators, new architectural components and functionalities will be required to aid not only human operators in mission planning, but also the unmanned aircraft systems themselves in the automatic generation, execution and partial verification of mission plans to achieve mission goals. This article proposes a formal framework and architecture based on the unifying concept of delegation that can be used for the automated specification, generation and execution of high-level collaborative missions involving one or more air vehicles platforms and human operators. We describe an agent-based software architecture, a temporal logic based mission specification language, a distributed temporal planner and a task specification language that when integrated provide a basis for the generation, instantiation and execution of complex collaborative missions on heterogeneous air vehicle systems. A prototype of the framework is operational in a number of autonomous unmanned aircraft systems developed in our research lab.
Stream-Based Hierarchical Anchoring.
K√ľnstliche Intelligenz, ??(??):??–??. Springer.
Publication status: Accepted
Autonomous systems situated in the real world often need to recognize, track, and reason about various types of physical objects. In order to allow reasoning at a symbolic level, one must create and continuously maintain a correlation between symbols denoting physical objects and sensor data being collected about them, a process called anchoring.In this paper we present a stream-based hierarchical anchoring framework. A classification hierarchy is associated with expressive conditions for hypothesizing the type and identity of an object given streams of temporally tagged sensor data. The anchoring process constructs and maintains a set of object linkage structures representing the best possible hypotheses at any time. Each hypothesis can be incrementally generalized or narrowed down as new sensor data arrives. Symbols can be associated with an object at any level of classification, permitting symbolic reasoning on different levels of abstraction. The approach is integrated in the DyKnow knowledge processing middleware and has been applied to an unmanned aerial vehicle traffic monitoring application.
Reports of the AAAI 2011 Spring Symposia.
The AI Magazine, 32(3):119–127. AAAI Press.
The Association for the Advancement of Artificial Intelligence presented the 2011 Spring Symposium Series Monday through Wednesday, March 21-23, 2011, at Stanford University. This report summarizes the eight symposia.
Optimal placement of UV-based communications relay nodes.
Journal of Global Optimization, 48(4):511–531. Springer.
Note: The original publication is available at www.springerlink.com:Oleg Burdakov, Patrick Doherty, Kaj Holmberg and Per-Magnus Olsson, Optimal placement of UV-based communications relay nodes, 2010, Journal of Global Optimization, (48), 4, 511-531.http://dx.doi.org/10.1007/s10898-010-9526-8Copyright: Springer Science Business Mediahttp://www.springerlink.com/
We consider a constrained optimization problem with mixed integer and real variables. It models optimal placement of communications relay nodes in the presence of obstacles. This problem is widely encountered, for instance, in robotics, where it is required to survey some target located in one point and convey the gathered information back to a base station located in another point. One or more unmanned aerial or ground vehicles (UAVs or UGVs) can be used for this purpose as communications relays. The decision variables are the number of unmanned vehicles (UVs) and the UV positions. The objective function is assumed to access the placement quality. We suggest one instance of such a function which is more suitable for accessing UAV placement. The constraints are determined by, firstly, a free line of sight requirement for every consecutive pair in the chain and, secondly, a limited communication range. Because of these requirements, our constrained optimization problem is a difficult multi-extremal problem for any fixed number of UVs. Moreover, the feasible set of real variables is typically disjoint. We present an approach that allows us to efficiently find a practically acceptable approximation to a global minimum in the problem of optimal placement of communications relay nodes. It is based on a spatial discretization with a subsequent reduction to a shortest path problem. The case of a restricted number of available UVs is also considered here. We introduce two label correcting algorithms which are able to take advantage of using some peculiarities of the resulting restricted shortest path problem. The algorithms produce a Pareto solution to the two-objective problem of minimizing the path cost and the number of hops. We justify their correctness. The presented results of numerical 3D experiments show that our algorithms are superior to the conventional Bellman-Ford algorithm tailored to solving this problem.
Relay Positioning for Unmanned Aerial Vehicle Surveillance.
The international journal of robotics research, 29(8):1069–1087. Sage Publications.
When unmanned aerial vehicles (UAVs) are used for surveillance, information must often be transmitted to a base station in real time. However, limited communication ranges and the common requirement of free line of sight may make direct transmissions from distant targets impossible. This problem can be solved using relay chains consisting of one or more intermediate relay UAVs. This leads to the problem of positioning such relays given known obstacles, while taking into account a possibly mission-specific quality measure. The maximum quality of a chain may depend strongly on the number of UAVs allocated. Therefore, it is desirable to either generate a chain of maximum quality given the available UAVs or allow a choice from a spectrum of Pareto-optimal chains corresponding to different trade-offs between the number of UAVs used and the resulting quality. In this article, we define several problem variations in a continuous three-dimensional setting. We show how sets of Pareto-optimal chains can be generated using graph search and present a new label-correcting algorithm generating such chains significantly more efficiently than the best-known algorithms in the literature. Finally, we present a new dual ascent algorithm with better performance for certain tasks and situations.
Bridging the sense-reasoning gap: DyKnow - Stream-based middleware for knowledge processing.
Advanced Engineering Informatics, 24(1):14–26. Elsevier.
Engineering autonomous agents that display rational and goal-directed behavior in dynamic physical environments requires a steady flow of information from sensors to high-level reasoning components. However, while sensors tend to generate noisy and incomplete quantitative data, reasoning often requires crisp symbolic knowledge. The gap between sensing and reasoning is quite wide, and cannot in general be bridged in a single step. Instead, this task requires a more general approach to integrating and organizing multiple forms of information and knowledge processing on different levels of abstraction in a structured and principled manner. We propose knowledge processing middleware as a systematic approach to organizing such processing. Desirable properties are presented and motivated. We argue that a declarative stream-based system is appropriate for the required functionality and present DyKnow, a concrete implemented instantiation of stream-based knowledge processing middleware with a formal semantics. Several types of knowledge processes are defined and motivated in the context of a UAV traffic monitoring application. In the implemented application, DyKnow is used to incrementally bridge the sense-reasoning gap and generate partial logical models of the environment over which metric temporal logical formulas are evaluated. Using such formulas, hypotheses are formed and validated about the type of vehicles being observed. DyKnow is also used to generate event streams representing for example changes in qualitative spatial relations, which are used to detect traffic violations expressed as declarative chronicles.
A Temporal Logic-based Planning and Execution Monitoring Framework for Unmanned Aircraft Systems.
Autonomous Agents and Multi-Agent Systems, 19(3):332–377. Springer.
Research with autonomous unmanned aircraft systems is reaching a new degree of sophistication where targeted missions require complex types of deliberative capability integrated in a practical manner in such systems. Due to these pragmatic constraints, integration is just as important as theoretical and applied work in developing the actual deliberative functionalities. In this article, we present a temporal logic-based task planning and execution monitoring framework and its integration into a fully deployed rotor-based unmanned aircraft system developed in our laboratory. We use a very challenging emergency services application involving body identification and supply delivery as a vehicle for showing the potential use of such a framework in real-world applications. TALplanner, a temporal logic-based task planner, is used to generate mission plans. Building further on the use of TAL (Temporal Action Logic), we show how knowledge gathered from the appropriate sensors during plan execution can be used to create state structures, incrementally building a partial logical model representing the actual development of the system and its environment over time. We then show how formulas in the same logic can be used to specify the desired behavior of the system and its environment and how violations of such formulas can be detected in a timely manner in an execution monitor subsystem. The pervasive use of logic throughout the higher level deliberative layers of the system architecture provides a solid shared declarative semantics that facilitates the transfer of knowledge between different modules.
Vision-Based Unmanned Aerial Vehicle Navigation Using Geo-Referenced Information.
EURASIP Journal on Advances in Signal Processing, 2009(387308):1–18. Hindawi Publishing Corporation.
This paper investigates the possibility of augmenting an Unmanned Aerial Vehicle (UAV) navigation system with a passive video camera in order to cope with long-term GPS outages. The paper proposes a vision-based navigation architecture which combines inertial sensors, visual odometry, and registration of the on-board video to a geo-referenced aerial image. The vision-aided navigation system developed is capable of providing high-rate and drift-free state estimation for UAV autonomous navigation without the GPS system. Due to the use of image-to-map registration for absolute position calculation, drift-free position performance depends on the structural characteristics of the terrain. Experimental evaluation of the approach based on offline flight data is provided. In addition the architecture proposed has been implemented on-board an experimental UAV helicopter platform and tested during vision-based autonomous flights.
Communication between agents with heterogeneous perceptual capabilities.
Information Fusion, 8(1):56–69. Elsevier.
In real world applications robots and software agents often have to be equipped with higher level cognitive functions that enable them to reason, act and perceive in changing, incompletely known and unpredictable environments. One of the major tasks in such circumstances is to fuse information from various data sources. There are many levels of information fusion, ranging from the fusing of low level sensor signals to the fusing of high level, complex knowledge structures. In a dynamically changing environment even a single agent may have varying abilities to perceive its environment which are dependent on particular conditions. The situation becomes even more complex when different agents have different perceptual capabilities and need to communicate with each other. In this paper, we propose a framework that provides agents with the ability to fuse both low and high level approximate knowledge in the context of dynamically changing environments while taking account of heterogeneous and contextually limited perceptual capabilities. To model limitations on an agent's perceptual capabilities we introduce the idea of partial tolerance spaces. We assume that each agent has one or more approximate databases where approximate relations are represented using lower and upper approximations on sets. Approximate relations are generalizations of rough sets. It is shown how sensory and other limitations can be taken into account when constructing and querying approximate databases for each respective agent. Complex relations inherit the approximativeness of primitive relations used in their definitions. Agents then query these databases and receive answers through the filters of their perceptual limitations as represented by (partial) tolerance spaces and approximate queries. The techniques used are all tractable. ¬© 2005 Elsevier B.V. All rights reserved.
A correspondence framework between three-valued logics and similarity-based approximate reasoning.
Fundamenta Informaticae, 75(1-4):179–193. IOS Press.
This paper focuses on approximate reasoning based on the use of similarity spaces. Similarity spaces and the approximated relations induced by them are a generalization of the rough set-based approximations of Pawlak [17, 18]. Similarity spaces are used to define neighborhoods around individuals and these in turn are used to define approximate sets and relations. In any of the approaches, one would like to embed such relations in an appropriate logic which can be used as a reasoning engine for specific applications with specific constraints. We propose a framework which permits a formal study of the relationship between approximate relations, similarity spaces and three-valued logics. Using ideas from correspondence theory for modal logics and constraints on an accessibility relation, we develop an analogous framework for three-valued logics and constraints on similarity relations. In this manner, we can provide a tool which helps in determining the proper three-valued logical reasoning engine to use for different classes of approximate relations generated via specific types of similarity spaces. Additionally, by choosing a three-valued logic first, the framework determines what constraints would be required on a similarity relation and the approximate relations induced by it. Such information would guide the generation of approximate relations for specific applications.
A flexible runtime system for image processing in a distributed computational environment for an unmanned aerial vehicle.
International Journal of Pattern Recognition and Artificial Intelligence, 20(5):763–780.
A runtime system for implementation of image processing operations is presented. It is designed for working in a flexible and distributed environment related to the software architecture of a newly developed UAV system. The software architecture can be characterized at a coarse scale as a layered system, with a deliberative layer at the top, a reactive layer in the middle, and a processing layer at the bottom. At a finer scale each of the three levels is decomposed into sets of modules which communicate using CORBA, allowing system development and deployment on the UAV to be made in a highly flexible way. Image processing takes place in a dedicated module located in the process layer, and is the main focus of the paper. This module has been designed as a runtime system for data flow graphs, allowing various processing operations to be created online and on demand by the higher levels of the system. The runtime system is implemented in Java, which allows development and deployment to be made on a wide range of hardware/software configurations. Optimizations for particular hardware platforms have been made using Java's native interface.
Probabilistic roadmap based path planning for an autonomous unmanned helicopter.
Journal of Intelligent & Fuzzy Systems, 17(4):395–405. IOS Press.
The emerging area of intelligent unmanned aerial vehicle (UAV) research has shown rapid development in recent years and offers a great number of research challenges for artificial intelligence. For both military and civil applications, there is a desire to develop more sophisticated UAV platforms where the emphasis is placed on development of intelligent capabilities. Imagine a mission scenario where a UAV is supplied with a 3D model of a region containing buildings and road structures and is instructed to fly to an arbitrary number of building structures and collect video streams of each of the building's respective facades. In this article, we describe a fully operational UAV platform which can achieve such missions autonomously. We focus on the path planner integrated with the platform which can generate collision free paths autonomously during such missions. Both probabilistic roadmap-based (PRM) and rapidly exploring random trees-based (RRT) algorithms have been used with the platform. The PRM-based path planner has been tested together with the UAV platform in an urban environment used for UAV experimentation.
A knowledge processing middleware framework and its relation to the JDL data fusion model.
Journal of Intelligent & Fuzzy Systems, 17(4):335–351. IOS Press.
Any autonomous system embedded in a dynamic and changing environment must be able to create qualitative knowledge and object structures representing aspects of its environment on the fly from raw or preprocessed sensor data in order to reason qualitatively about the environment and to supply such state information to other nodes in the distributed network in which it is embedded. These structures must be managed and made accessible to deliberative and reactive functionalities whose successful operation is dependent on being situationally aware of the changes in both the robotic agent's embedding and internal environments. DyKnow is a knowledge processing middleware framework which provides a set of functionalities for contextually creating, storing, accessing and processing such structures. The framework is implemented and has been deployed as part of a deliberative/reactive architecture for an autonomous unmanned aerial vehicle. The architecture itself is distributed and uses real-time CORBA as a communications infrastructure. We describe the system and show how it can be used to create more abstract entity and state representations of the world which can then be used for situation awareness by an unmanned aerial vehicle in achieving mission goals. We also show that the framework is a working instantiation of many aspects of the JDL data fusion model.
Approximate Databases: A support tool for approximate reasoning.
Journal of applied non-classical logics, 16(1-2):87–118. √Čditions Herm√®s-Lavoisier.
Note: Special issue on implementation of logics
This paper describes an experimental platform for approximate knowledge databases called the Approximate Knowledge Database (AKDB), based on a semantics inspired by rough sets. The implementation is based upon the use of a standard SQL database to store logical facts, augmented with several query interface layers implemented in JAVA through which extensional, intensional and local closed world nonmonotonic queries in the form of crisp or approximate logical formulas can be evaluated tractably. A graphical database design user interface is also provided which simplifies the design of databases, the entering of data and the construction of queries. The theory and semantics for AKDBs is presented in addition to application examples and details concerning the database implementation.
DyKnow: An approach to middleware for knowledge processing.
Journal of Intelligent & Fuzzy Systems, 15(1):3–13. IOS Press.
Any autonomous system embedded in a dynamic and changing environment must be able to create qualitative knowledge and object structures representing aspects of its environment on the fly from raw or preprocessed sensor data in order to reason qualitatively about the environment. These structures must be managed and made accessible to deliberative and reactive functionalities which are dependent on being situationally aware of the changes in both the robotic agent's embedding and internal environment. DyKnow is a software framework which provides a set of functionalities for contextually accessing, storing, creating and processing such structures. The system is implemented and has been deployed in a deliberative/reactive architecture for an autonomous unmanned aerial vehicle. The architecture itself is distributed and uses real-time CORBA as a communications infrastructure. We describe the system and show how it can be used in execution monitoring and chronicle recognition scenarios for UAV applications.
Issues in Designing Physical Agents for Dynamic Real-Time Environments: World Modeling, Planning, Learning, and Communicating.
The AI Magazine, 25(2):137–138. AAAI Press.
This article discusses a workshop held in conjunction with the Eighteenth International Joint Conference on Artificial Intelligence (IJCAI-03), held in Acapulco, Mexico, on 11 August 2003.
Towards a framework for approximate ontologies.
Fundamenta Informaticae, 57(2-4):147–165. IOS Press.
Currently, there is a great deal of interest in developing tools for the generation and use of ontologies on the WWW. These knowledge structures are considered essential to the success of the semantic web, the next phase in the evolution of the WWW. Much recent work with ontologies assumes that the concepts used as building blocks are crisp as opposed to approximate. It is a premise of this paper that approximate concepts and ontologies will become increasingly more important as the semantic web becomes a reality. We propose a framework for specifying, generating and using approximate ontologies. More specifically, (1) a formal framework for defining approximate concepts, ontologies and operations on approximate concepts and ontologies is presented. The framework is based on intuitions from rough set theory, (2) algorithms for automatically generating approximate ontologies from traditional crisp ontologies or from large data sets together with additional knowledge are presented. The knowledge will generally be related to similarity measurements between individual objects in the data sets, or constraints of a logical nature which rule out particular constellations of concepts and dependencies in generated ontologies. The techniques for generating approximate ontologies are parameterizable. The paper provides specific instantiations and examples.
2003 AAAI Spring Symposium Series.
The AI Magazine, 24(3):131–140. AAAI Press.
The American Association for Artificial Intelligence, in cooperation with Stanford University‚Äôs Department of Computer Science, presented the 2003 Spring Symposium Series, Monday through Wednesday, 24‚Äď26 March 2003, at Stanford University. The titles of the eight symposia were Agent-Mediated Knowledge Management, Computational Synthesis: From Basic Building Blocks to High- Level Functions, Foundations and Applications of Spatiotemporal Reasoning (FASTR), Human Interaction with Autonomous Systems in Complex Environments, Intelligent Multimedia Knowledge Management, Logical Formalization of Commonsense Reasoning, Natural Language Generation in Spoken and Written Dialogue, and New Directions in Question-Answering Motivation.
TALPLANNER - A temporal logic-based planner.
The AI Magazine, 22(3):95–102. AAAI Press.
TALPLANNER is a forward-chaining planner that utilizes domain-dependent knowledge to control search in the state space generated by action invocation. The domain-dependent control knowledge, background knowledge, plans, and goals are all represented, using,formulas in, a temporal logic called TAL, which has been developed independently as a formalism for specifying agent narratives and reasoning about them. In the Fifth International Artificial Intelligence Planning and Scheduling Conference planning competition, TALPLANNER exhibited impressive performance, winning the Outstanding Performance Award in the Domain-Dependent Planning Competition. In this article, we provide an overview of TALPLANNER.
TALplanner: A temporal logic based forward chaining planner.
Annals of Mathematics and Artificial Intelligence, 30(1-4):119–169. Springer.
We present TALplanner, a forward-chaining planner based on the use of domain-dependent search control knowledge represented as formulas in the Temporal Action Logic (TAL). TAL is a narrative based linear metric time logic used for reasoning about action and change in incompletely specified dynamic environments. TAL is used as the formal semantic basis for TALplanner, where a TAL goal narrative with control formulas is input to TALplanner which then generates a TAL narrative that entails the goal and control formulas. The sequential version of TALplanner is presented. The expressivity of plan operators is then extended to deal with an interesting class of resource types. An algorithm for generating concurrent plans, where operators have varying durations and internal state, is also presented. All versions of TALplanner have been implemented. The potential of these techniques is demonstrated by applying TALplanner to a number of standard planning benchmarks in the literature.
The PMA and relativizing minimal change for action update.
Fundamenta Informaticae, 44(1-2):95–131. IOS Press.
Recently, a great deal of progress has been made using nonmonotonic temporal logics to formalize reasoning about action and change. In particular, much focus has been placed on the proper representation of non-deterministic actions and the indirect effects of actions. For the latter the use of causal or fluent dependency rule approaches has been dominant. Although much recent effort has also been spent applying the belief revision/update (BR/U) approach to the action and change domain, there has been less progress in dealing with nondeterministic update and indirect effects represented as integrity constraints. We demonstrate that much is to be gained by cross-fertilization between the two paradigms and we show this in the following manner. We first propose a generalization of the PMA, called the modified MPMA which uses intuitions from the TL paradigm to permit representation of nondeterministic update and the use of integrity constraints interpreted as causal or fluent dependency rules. We provide several syntactic characterizations of MPMA, one of which is in terms of a simple temporal logic and provide a representation theorem showing equivalence between the two. In constructing the MPMA, we discovered a syntactic anomaly which we call the redundant atom anomaly that many TL approaches suffer from. We provide a method for avoiding the problem which is equally applicable across paradigms. We also describe a syntactic characterization of MPMA in terms of Dijkstra semantics. We set up a framework for future generalization of the BR/U approach and conclude with a formal comparison of related approaches.
Tackling the qualification problem using fluent dependency constraints.
Computational intelligence, 16(2):169–209. Blackwell Publishing.
In the area of formal reasoning about action and change, one of the fundamental representation problems is providing concise modular and incremental specifications of action types and world models, where instantiations of action types are invoked by agents such as mobile robots. Provided the preconditions to the action are true, their invocation results in changes to the world model concomitant with the goal-directed behavior of the agent. One particularly difficult class of related problems, collectively called the qualification problem, deals with the need to find a concise incremental and modular means of characterizing the plethora of exceptional conditions that might qualify an action, but generally do not, without having to explicitly enumerate them in the preconditions to an action. We show how fluent dependency constraints together with the use of durational fluents can be used to deal with problems associated with action qualification using a temporal logic for action and change called TAL-Q. We demonstrate the approach using action scenarios that combine solutions to the frame, ramification, and qualification problems in the context of actions with duration, concurrent actions, nondeterministic actions, and the use of both Boolean and non-Boolean fluents. The circumscription policy used for the combined problems is reducible to the first-order case.
Meta-queries on deductive databases.
Fundamenta Informaticae, 40(1):17–30. IOS Press.
We introduce the notion of a meta-query on relational databases and a technique which can be used to represent and solve a number of interesting problems from the area of knowledge representation using logic. The technique is based on the use of quantifier elimination and may also be used to query relational databases using a declarative query language called SHQL (Semi-Horn Query Language), introduced in . SHQL is a fragment of classical first-order predicate logic and allows us to define a query without supplying its explicit definition. All SHQL queries to the database can be processed in polynomial time (both on the size of the input query and the size of the database). We demonstrate the use of the technique in problem solving by structuring logical puzzles from the Knights and Knaves domain as SHQL meta-queries on relational databases. We also provide additional examples demonstrating the flexibility of the technique. We conclude with a description of a newly developed software tool, The Logic Engineer, which aids in the description of algorithms using transformation and reduction techniques such as those applied in the meta-querying approach.
Declarative PTIME queries for relational databases using quantifier elimination.
Journal of logic and computation (Print), 9(5):737–758. Oxford University Press.
In this paper, we consider the problem of expressing and computing queries on relational deductive databases in a purely declarative query language, called SHQL (Semi-Horn Query Language). Assuming the relational databases in question are ordered, we show that all SHQL queries are computable in PTIME (polynomial time) and the whole class of PTIME queries is expressible in SHQL. Although similar results have been proven for fixpoint languages and extensions to datalog, the claim is that SHQL has the advantage of being purely declarative, where the negation operator is interpreted as classical negation, mixed quantifiers may be used and a query is simply a restricted first-order theory not limited by the rule-based syntactic restrictions associated with logic programs in general. We describe the PTIME algorithm used to compute queries in SHQL which is based in part on quantifier elimination techniques and also consider extending the method to incomplete relational databases using intuitions related to circumscription techniques.
(TAL) temporal action logics: Language specification and tutorial.
Electronic Transactions on Artifical Intelligence, 2(3-4):273–306.
The purpose of this article is to provide a uniform, lightweight language specication and tutorial for a class of temporal logics for reasoning about action and change that has been developed by our group during the period 1994-1998. The class of logics are collected under the name TAL, an acronym for Temporal Action Logics. TAL has its origins and inspiration in the work with Features and Fluents (FF) by Sandewall, but has diverged from the methodology and approach through the years. We first discuss distinctions and compatibility with FF, move on to the lightweight language specication, and then present a tutorial in terms of an excursion through the different parts of a relatively complex narrative defined using TAL. We conclude with an annotated list of published work from our group. The article tries to strike a reasonable balance between detail and readability, making a number of simplications regarding narrative syntax and translation to a base logical language. Full details are available in numerous technical reports and articles which are listed in the final section of this article.
General domain circumscription and its effective reductions.
Fundamenta Informaticae, 36(1):23–55. IOS Press.
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 show that for a certain class of domain circumscribed theories, 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.
Computing circumscription revisited: A reduction algorithm.
Journal of automated reasoning, 18(3):297–336. Kluwer Academic Publishers.
In recent years, a great deal of attention has been devoted to logics of common-sense reasoning. Among the candidates proposed, circumscription has been perceived as an elegant mathematical technique for modeling nonmonotonic reasoning, but difficult to apply in practice. The major reason for this is the second-order nature of circumscription axioms and the difficulty in finding proper substitutions of predicate expressions for predicate variables. One solution to this problem is to compile, where possible, second-order formulas into equivalent first-order formulas. Although some progress has been made using this approach, the results are not as strong as one might desire and they are isolated in nature. In this article, we provide a general method that can be used in an algorithmic manner to reduce certain circumscription axioms to first-order formulas. The algorithm takes as input an arbitrary second-order formula and either returns as output an equivalent first-order formula, or terminates with failure. The class of second-order formulas, and analogously the class of circumscriptive theories that can be reduced, provably subsumes those covered by existing results. We demonstrate the generality of the algorithm using circumscriptive theories with mixed quantifiers (some involving Skolemization), variable constants, nonseparated formulas, and formulas with n-ary predicate variables. In addition, we analyze the strength of the algorithm, compare it with existing approaches, and provide formal subsumption results.
A reduction result for circumscribed semi-horn formulas.
Fundamenta Informaticae, 28(3,4):261–272. IOS Press.
Circumscription has been perceived as an elegant mathematical technique for modeling nonmonotonic and commonsense reasoning, but difficult to apply in practice due to the use of second-order formulas. One proposal for dealing with the computational problems is to identify classes of first-order formulas whose circumscription can be shown to be equivalent to a first-order formula. In previous work, we presented an algorithm which reduces certain classes of second-order circumscription axioms to logically equivalent first-order formulas. The basis for the algorithm is an elimination lemma due to Ackermann. In this paper, we capitalize on the use of a generalization of Ackermann's Lemma in order to deal with a subclass of universal formulas called <em>semi-Horn formulas</em>. Our results subsume previous results by Kolaitis and Papadimitriou regarding a characterization of circumscribed definite logic programs which are first-order expressible. The method for distinguishing which formulas are reducible is based on a boundedness criterion. The approach we use is to first reduce a circumscribed semi-Horn formula to a fixpoint formula which is reducible if the formula is bounded, otherwise not. In addition to a number of other extensions, we also present a fixpoint calculus which is shown to be sound and complete for bounded fixpoint formulas.
Fuzzy if-then-unless rules and their implementation.
International Journal of Uncertainty Fuzziness and Knowledge-Based Systems, 1(2):167–182. World Scientific.
We consider the possibility of generalizing the notion of a fuzzy If-Then rule to take into account its context dependent nature. We interpret fuzzy rules as modeling a forward directed causal relationship between the antecedent and the conclusion, which applies in most contexts, but on occasion breaks down in exceptional contexts. The default nature of the rule is modeled by augmenting the original If-Then rule with an exception part. We then consider the proper semantic correlate to such an addition and propose a ternary relation which satisfies a number of intuitive constraints described in terms of a number of inference rules. In the rest of the paper, we consider implementational issues arising from the unless extension and propose the use of reason maintenance systems, in particular TMS's, where a fuzzy If-Then-Unless rule is encoded into a dependency net. We verify that the net satisfies the constraints stated in the inference schemes and conclude with a discussion concerning the integration of qualitative IN-OUT labelings of the TMS with quantitative degree of membership labelings for the variables in question.
NML-3 - A non-monotonic logic with explicit defaults.
Journal of applied non-classical logics, 2(1):9–48. √Čditions Herm√®s-Lavoisier.