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ManyValued Modal Logics
 Fundamenta Informaticae
, 1992
"... . Two families of manyvalued modal logics are investigated. Semantically, one family is characterized using Kripke models that allow formulas to take values in a finite manyvalued logic, at each possible world. The second family generalizes this to allow the accessibility relation between worlds a ..."
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Cited by 271 (16 self)
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. Two families of manyvalued modal logics are investigated. Semantically, one family is characterized using Kripke models that allow formulas to take values in a finite manyvalued logic, at each possible world. The second family generalizes this to allow the accessibility relation between worlds also to be manyvalued. Gentzen sequent calculi are given for both versions, and soundness and completeness are established. 1 Introduction The logics that have appeared in artificial intelligence form a rich and varied collection. While classical (and maybe intuitionistic) logic su#ces for the formal development of mathematics, artificial intelligence has found uses for modal, temporal, relevant, and manyvalued logics, among others. Indeed, I take it as a basic principle that an application should find (or create) an appropriate logic, if it needs one, rather than reshape the application to fit some narrow class of `established' logics. In this paper I want to enlarge the variety of logics...
Signed Formula Logic Programming: Operational Semantics and Applications
, 1995
"... . Signed formula can be used to reason about a wide variety of multiplevalued logics. The formal theoretical foundation of logic programming based on signed formulas is developed in [26]. In this paper, the operational semantics of signed formula logic programming is investigated through constraint ..."
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. Signed formula can be used to reason about a wide variety of multiplevalued logics. The formal theoretical foundation of logic programming based on signed formulas is developed in [26]. In this paper, the operational semantics of signed formula logic programming is investigated through constraint logic programming. Applications to bilattice logic programming and truthmaintenance are considered. Keywords: Logic for Artificial Intelligence, Multiplevalued Logic, Signed Formula, Constraint Logic Programming, TruthMaintenance, Bilattices * Please address all correspondence to: James Lu Department of Computer Science Bucknell University Lewisburg, PA 17837 U.S.A. Email: jameslu@bucknell.edu Phone: +1 717 524 1394 Fax: +1 717 524 1822 ** Work supported in part by the NSF under Grant CCR9225037. SIGNED FORMULA LOGIC PROGRAMMING 1 1. Introduction The logic of signed formulas facilitates the examination of questions regarding multiplevalued logics through classical logic. As...
Amalgamating Knowledge Bases, II: Distributed Mediators
 Journal of Intelligent and Cooperative Information Systems
, 1994
"... Integrating knowledge from multiple sources is an important aspect of automated reasoning systems. In [23], we presented a uniform declarative and operational framework, based on annotated logics, for amalgamating multiple knowledge bases and data structures (e.g. relational, objectoriented, spatia ..."
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Cited by 6 (2 self)
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Integrating knowledge from multiple sources is an important aspect of automated reasoning systems. In [23], we presented a uniform declarative and operational framework, based on annotated logics, for amalgamating multiple knowledge bases and data structures (e.g. relational, objectoriented, spatial, and temporal structures) when these knowledge bases (possibly) contain inconsistencies, uncertainties, and nonmonotonic modes of negation. We showed that annotated logics may be used, with some modifications, to mediate between different knowledge bases. The multiple knowledge bases are amalgamated by embedding the individual knowledge bases into a lattice. In this paper, we describe how, given a network of sites where the different databases reside, it is possible to define a distributed semantics for amalgamated knowledge bases. More importantly, we study how the mediator may be distributed across multiple sites so that when certain conditions are satisfied, network failures do not af...
M.: Extending MultipleValued Clausal Forms with Linear Integer Arithmetic
 In: ISMVL
, 2011
"... We extend the language of signed manyvalued clausal forms with linear integer arithmetic constraints. In this way, we get a simple modeling language in which a wide range of practical combinatorial problems admit compact and natural encodings. We then define efficient translations from our languag ..."
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We extend the language of signed manyvalued clausal forms with linear integer arithmetic constraints. In this way, we get a simple modeling language in which a wide range of practical combinatorial problems admit compact and natural encodings. We then define efficient translations from our language into the SAT and SMT formalism, and propose to use SAT and SMT solvers for finding solutions. 1
On Nonclausal Hornlike Satisfiability Problems
, 2005
"... Satisfactibilidad de problemas no clausales con estructura Horn Tesis que presenta ..."
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Satisfactibilidad de problemas no clausales con estructura Horn Tesis que presenta
Some Applications Of Non Clausal Deduction
, 1995
"... In this thesis it is shown that by using negation normal form for representing propositional formulas, rather than clause forms such as conjunctive and disjunctive normal forms, reasoning systems that are more efficent for many classes of formulas can be built. This is due the fact that the process ..."
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In this thesis it is shown that by using negation normal form for representing propositional formulas, rather than clause forms such as conjunctive and disjunctive normal forms, reasoning systems that are more efficent for many classes of formulas can be built. This is due the fact that the process of converting arbitrary propositional formulas into clause forms is an expensive computational task. Algorithms for two related problems in artificial intelligence, namely computing prime implicates and implicants, and computing minimal diagnoses are developed and implemented. These algorithms use negation normal form for representing proportional formulas. These algorithms are based on dissolution, an inference rule for negation normal form. Through theoretical and experimental analysis it is shown that these algorithms are superior to many clausebased algorithms. Antilinks are defined and certain operations based on them are introduced. By performing these operations, many nonprime implicants/implicates and many nonminimal diagnoses can be eliminated without doing expensive subsumption checks. Experimental results showing significant improvements obtained by using these operations are also given. An algorithm for computing prime implicants and implicates of multiplevalued logics is also developed. This algorithm is based on signed dissolution, an inference rule for multiplevalued logics. Acknowledgments I am deeply indebted to my thesis advisor Professor Neil V. Murray, for suggesting the topic to me, and for providing suggestions and comments which were crucial in the development of this thesis. He also introduced me to the exciting topic of automated reasoning. His constructive criticism helped in improving my writing and presentation skills. I would also like ...