271 research outputs found
Complexity of Nested Circumscription and Nested Abnormality Theories
The need for a circumscriptive formalism that allows for simple yet elegant
modular problem representation has led Lifschitz (AIJ, 1995) to introduce
nested abnormality theories (NATs) as a tool for modular knowledge
representation, tailored for applying circumscription to minimize exceptional
circumstances. Abstracting from this particular objective, we propose L_{CIRC},
which is an extension of generic propositional circumscription by allowing
propositional combinations and nesting of circumscriptive theories. As shown,
NATs are naturally embedded into this language, and are in fact of equal
expressive capability. We then analyze the complexity of L_{CIRC} and NATs, and
in particular the effect of nesting. The latter is found to be a source of
complexity, which climbs the Polynomial Hierarchy as the nesting depth
increases and reaches PSPACE-completeness in the general case. We also identify
meaningful syntactic fragments of NATs which have lower complexity. In
particular, we show that the generalization of Horn circumscription in the NAT
framework remains CONP-complete, and that Horn NATs without fixed letters can
be efficiently transformed into an equivalent Horn CNF, which implies
polynomial solvability of principal reasoning tasks. Finally, we also study
extensions of NATs and briefly address the complexity in the first-order case.
Our results give insight into the ``cost'' of using L_{CIRC} (resp. NATs) as a
host language for expressing other formalisms such as action theories,
narratives, or spatial theories.Comment: A preliminary abstract of this paper appeared in Proc. Seventeenth
International Joint Conference on Artificial Intelligence (IJCAI-01), pages
169--174. Morgan Kaufmann, 200
Representing First-Order Causal Theories by Logic Programs
Nonmonotonic causal logic, introduced by Norman McCain and Hudson Turner,
became a basis for the semantics of several expressive action languages.
McCain's embedding of definite propositional causal theories into logic
programming paved the way to the use of answer set solvers for answering
queries about actions described in such languages. In this paper we extend this
embedding to nondefinite theories and to first-order causal logic.Comment: 29 pages. To appear in Theory and Practice of Logic Programming
(TPLP); Theory and Practice of Logic Programming, May, 201
Methods for Solving Necessary Equivalences
Nonmonotonic Logics such as Autoepistemic Logic, Reflective Logic, and Default Logic, are usually
defined in terms of set-theoretic fixed-point equations defined over deductively closed sets of sentences of First
Order Logic. Such systems may also be represented as necessary equivalences in a Modal Logic stronger than
S5 with the added advantage that such representations may be generalized to allow quantified variables crossing
modal scopes resulting in a Quantified Autoepistemic Logic, a Quantified Autoepistemic Kernel, a Quantified
Reflective Logic, and a Quantified Default Logic. Quantifiers in all these generalizations obey all the normal laws
of logic including both the Barcan formula and its converse. Herein, we address the problem of solving some
necessary equivalences containing universal quantifiers over modal scopes. Solutions obtained by these
methods are then compared to related results obtained in the literature by Circumscription in Second Order Logic
since the disjunction of all the solutions of a necessary equivalence containing just normal defaults in these
Quantified Logics, is equivalent to that system
Semantic Matchmaking of Web Resources with Local Closed-World Reasoning
Ontology languages like OWL allow for semantically rich annotation of resources (e.g., products advertised at on-line electronic marketplaces). The description logic (DL) formalism underlying OWL provides reasoning techniques that perform match-making on such annotations. This paper identifies peculiarities in the use of DL inferences for matchmaking that derive from OWL\u27s open-world semantics, analyzes local closed-world reasoning for its applicability to matchmaking, and investigates the suitability of two nonmonotonic extensions to DL, autoepistemic DLs and DLs with circumscription, for local closed-world reasoning in the matchmaking context. An elaborate example of an electronic marketplace for PC product catalogs from the e-commerce domain demonstrates how these formalisms can be used to realize such scenarios
Modularity in answer set programs
Answer set programming (ASP) is an approach to rule-based constraint programming allowing flexible knowledge representation in variety of application areas. The declarative nature of ASP is reflected in problem solving. First, a programmer writes down a logic program the answer sets of which correspond to the solutions of the problem. The answer sets of the program are then computed using a special purpose search engine, an ASP solver. The development of efficient ASP solvers has enabled the use of answer set programming in various application domains such as planning, product configuration, computer aided verification, and bioinformatics.
The topic of this thesis is modularity in answer set programming. While modern programming languages typically provide means to exploit modularity in a number of ways to govern the complexity of programs and their development process, relatively little attention has been paid to modularity in ASP. When designing a module architecture for ASP, it is essential to establish full compositionality of the semantics with respect to the module system. A balance is sought between introducing restrictions that guarantee the compositionality of the semantics and enforce a good programming style in ASP, and avoiding restrictions on the module hierarchy for the sake of flexibility of knowledge representation.
To justify a replacement of a module with another, that is, to be able to guarantee that changes made on the level of modules do not alter the semantics of the program when seen as an entity, a notion of equivalence for modules is provided. In close connection with the development of the compositional module architecture, a transformation from verification of equivalence to search for answer sets is developed. The translation-based approach makes it unnecessary to develop a dedicated tool for the equivalence verification task by allowing the direct use of existing ASP solvers.
Translations and transformations between different problems, program classes, and formalisms are another central theme in the thesis. To guarantee efficiency and soundness of the translation-based approach, certain syntactical and semantical properties of transformations are desirable, in terms of translation time, solution correspondence between the original and the transformed problem, and locality/globality of a particular transformation.
In certain cases a more refined notion of minimality than that inherent in ASP can make program encodings more intuitive. Lifschitz' parallel and prioritized circumscription offer a solution in which certain atoms are allowed to vary or to have fixed values while others are falsified as far as possible according to priority classes. In this thesis a linear and faithful transformation embedding parallel and prioritized circumscription into ASP is provided. This enhances the knowledge representation capabilities of answer set programming by allowing the use of existing ASP solvers for computing parallel and prioritized circumscription
Commonsense axiomatizations for logic programs
AbstractVarious semantics for logic programs with negation are described in terms of a dualized program together with additional axioms, some of which are second-order formulas. The semantics of Clark, Fitting, and Kunen are characterized in this framework, and a finite first-order presentation of Kunen's semantics is described. A new axiom to represent “commonsense” reasoning is proposed for logic programs. It is shown that the well-founded semantics and stable models are definable with this axiom. The roles of domain augmentation and domain closure are examined. A “domain foundation” axiom is proposed to replace the domain closure axiom
Two new strategies for inconsistency-adaptive logics
In this paper I present two new strategies for inconsistency adaptive logics: the reliable sufficient information strategy of ACLuN3 and the minimally abnormal sufficient information strategy of ACLuN4. I give proof theory and semantics for both ACLuN3 and ACLuN4. I also compare them with the well-known inconsistency-adaptive logics ACLuN1 and ACLuN2
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