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Strong and uniform equivalence of nonmonotonic theories – an algebraic approach

Mirosław Truszczyński
2007 Annals of Mathematics and Artificial Intelligence  
We show that the concepts of strong and uniform equivalence of logic programs can be generalized to an abstract algebraic setting of operators on complete lattices.  ...  Our results imply characterizations of strong and uniform equivalence for several nonmonotonic logics including logic programming with aggregates, default logic and a version of autoepistemic logic.  ...  Our main contribution is an algebraic account of strong and uniform equivalence in terms of operators on complete lattices.  ... 
doi:10.1007/s10472-007-9049-2 fatcat:wresng47vrdh3ivwwoefsst6gy

Strong Equivalence of Nonmonotonic Theories -- an Algebraic Approach

Mirek Truszczynski
2006 International Symposium on Artificial Intelligence and Mathematics  
We show that the concept of strong equivalence of logic programs can be generalized to an abstract algebraic setting of operators on complete lattices.  ...  Our results imply characterizations of strong equivalence for several nonmonotonic logics including logic programming with aggregates, default logic and a version of autoepistemic logic.  ...  Acknowledgments We acknowledge the support of NSF grant IIS-0325063.  ... 
dblp:conf/isaim/Truszczynski06 fatcat:vivwfied7zhtvjxl7ubglrfkzi

Page 5955 of Mathematical Reviews Vol. , Issue 2004h [page]

2004 Mathematical Reviews  
Then, we prove that the categories MV and MV“, whose objects are MV-algebras and MV*-algebras respectively, with their corresponding morphisms, are equivalent.  ...  Most of the paper is the presentation of an axiomatic system and its properties, mainly what can be deduced.  ... 

Hyperequivalence of Programs and Operators

Miroslaw Truszczynski, Stefan Woltran
2008 International Symposium on Artificial Intelligence and Mathematics  
Recent research in nonmonotonic logic programming has focused on different notions of program equivalence relevant for program optimization and modular programming.  ...  We then use some of our results in order to obtain characterizations of the equivalence of theories in Moore's autoepistemic logic.  ...  This gives rise to a common view on strong and uniform equivalence as discussed in (Woltran 2007) .  ... 
dblp:conf/isaim/TruszczynskiW08 fatcat:s6gxxvntlbgllif4yrguua5h5e

Page 2866 of Mathematical Reviews Vol. , Issue 2003d [page]

2003 Mathematical Reviews  
We show how to enrich the syntax and proof theory of HH with the help of a given constraint system, in such a way that the key property of HH as a logic programming language (namely, the existence of uniform  ...  The author shows that Pos is a complete sub-Heyting algebra of the Heyting algebra of sets of substitutions, closed under instantiation.  ... 

The complexity of constraint satisfaction: an algebraic approach [chapter]

Andrei Krokhin, Andrei Bulatov, Peter Jeavons
Structural Theory of Automata, Semigroups, and Universal Algebra  
In this survey paper we discuss an algebraic approach that has proved to be very successful in studying the complexity of constraint problems.  ...  In database theory, it has been shown that the key problem of conjunctive-query evaluation can be viewed as  ...  An algebra is said to be uniform if, for any subalgebra B, the blocks of every congruence of B are of the same size. Clearly, all two-element algebras, groups and quasi-groups are uniform.  ... 
doi:10.1007/1-4020-3817-8_8 fatcat:pk3bbgore5a4zdhj35fhnr7kum

Interpretability and Equivalence in Quantified Equilibrium Logic

David Pearce, Agustín Valverde
2007 International Conference on Logic Programming and Non-Monotonic Reasoning  
The study of synonymy among propositional theories in equilibrium logic, begun in [36] , is extended to the first-order case.  ...  Theorem 1 (Strong Equivalence of theories, [23] ).  ...  The first systematic treatments of synonymous theories in this context can be found in [3, 4] , a more algebraic approach can be found in [20] .  ... 
dblp:conf/lpnmr/PearceV07 fatcat:hsux2jyqzzemfcki724vqddjka

Nonmonotonic Logics and Their Algebraic Foundations [chapter]

Mirosław Truszczyński
2006 Lecture Notes in Computer Science  
We then point out to algebraic principles behind the two logics and present an abstract algebraic theory that unifies them and provides an effective framework to study properties of nonmonotonic reasoning  ...  We briefly discuss motivations that led to the emergence of nonmonotonic logics and introduce two major nonmonotonic formalisms, default and autoepistemic logics.  ...  Acknowledgments We acknowledge the support of NSF grant IIS-0325063 and KSEF grant 1036-RDE-008.  ... 
doi:10.1007/11874683_4 fatcat:u7klqrtejfe43c67l2vm2ga5x4

Hyperequivalence of logic programs with respect to supported models

Mirosław Truszczyński, Stefan Woltran
2008 Annals of Mathematics and Artificial Intelligence  
Recent research in nonmonotonic logic programming has focused on program equivalence relevant for program optimization and modular programming.  ...  In this paper, we consider a framework of equivalence notions for logic programs under the supported (minimal) modelsemantics and provide characterizations for this framework in model-theoretic terms.  ...  Acknowledgments This work was partially supported by the NSF grant IIS-0325063, the KSEF grant KSEF-1036-RDE-008, and by the Austrian Science Fund (FWF) under grant P18019.  ... 
doi:10.1007/s10472-009-9119-8 fatcat:md6tnk3jzranrcz3mfmsqilnw4

JSL volume 65 issue 4 Cover and Back matter

2000 Journal of Symbolic Logic (JSL)  
On fixed-point logic with counting 777 FONT, JOSEP MARIA and Rius, MIQUEL. An abstract algebraic logic approach to tetravalent modal logics 481 FOUCHE, WILLEM.  ...  A note on uniform definability and minimal fields of definition 817 NEMETI, ISTVAN and SAGI, GABOR. On the equational theory of representable polyadic equality algebras 1143 NAGAYAMA, MISAO.  ...  Identity crises and strong compactness, by ARTHUR W.  ... 
doi:10.1017/s0022481200011439 fatcat:2qicizggf5d3lba23vkswfiaii

Page 7306 of Mathematical Reviews Vol. , Issue 97M [page]

1997 Mathematical Reviews  
Preferential structures play an important role in various systems of nonmonotonic reasoning.  ...  In the author’s view, one of the advantages of the relational approach consists in the gain of compositionality.  ... 

Synonymous theories and knowledge representations in answer set programming

D. Pearce, A. Valverde
2012 Journal of computer and system sciences (Print)  
This paper proposes and studies a concept of synonymy that applies to equivalent theories formulated in distinct vocabularies.  ...  This serves as an adequate formal foundation for ASP and allows us to obtain a logical account of the synonymy relation.  ...  Acknowledgments We are very grateful to Michael Gelfond for suggesting the case study treated in Section 6 and for commenting on an earlier draft of this paper.  ... 
doi:10.1016/j.jcss.2011.02.013 fatcat:uzqb2sln2zc3bph2titjpvhmmu

Defaults and Infinitesimals: Defeasible Inference by Nonarchimedean Entropy-Maximization [article]

Emil Weydert
2013 arXiv   pre-print
constraints and on a preferred-model implementation of entropy maximization.  ...  We develop a new semantics for defeasible inference based on extended probability measures allowed to take infinitesimal values, on the interpretation of defaults as generalized conditional probability  ...  An L-theory Ti s called model-complete iff for any pair ofT -models M and N, if N is an extension of M, then N is an elementary extension of M, i.e. every L-sentence with parameters from M is true in N  ... 
arXiv:1302.4988v1 fatcat:q55wyeuvcberde6hkrp6zelqey

Master Index—Volumes 141–150

2003 Artificial Intelligence  
Perny Qualitative decision theory with preference relations and comparative uncertainty: An axiomatic approach 148 (2003) 219-260 Dubois, D. and H.  ...  Truszczyński Uniform semantic treatment of default and autoepistemic logics 143 (2003) 79-122 de Weerdt, M., see Tonino, H. 142 (2002) 121-145 Dimopoulos, Y., B. Nebel and F.  ... 
doi:10.1016/s0004-3702(03)00182-6 fatcat:connrcrjpfhqtesbrxfaow4rhq

Forthcoming Papers

2002 Journal of Logic and Computation  
More precisely, we prove that if Ä is a graded modal logic then a pair´ µ of graded formulae in Ä have an interpolant in Ä if, and only if, entails along elementary equivalence with respect to Ä.  ...  It is well known that interpolation fails in general for these logics and it is then natural to ask for a semantical characterization (stronger than entailment) of pairs of graded formulae having an interpolant  ...  Future issues Special Issue on Frontiers of Revision and Contraction: The Third De Morgan Workshop Controlled Revision: An Algorithmic Approach for Belief Revision D. M. Gabbay, G. Pigozzi and J.  ... 
doi:10.1093/logcom/12.6.1107 fatcat:gprb33g5q5czzoa5x55jsqnndi
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