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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 215 (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...
Model Checking Partial State Spaces with 3Valued Temporal Logics (Extended Abstract)
 In Proceedings of the 11th Conference on Computer Aided Verification
, 1999
"... ) Glenn Bruns and Patrice Godefroid Bell Laboratories, Lucent Technologies fgrb,godg@belllabs.com Abstract. We address the problem of relating the result of model checking a partial state space of a system to the properties actually possessed by the system. We represent incomplete state space ..."
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Cited by 95 (7 self)
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) Glenn Bruns and Patrice Godefroid Bell Laboratories, Lucent Technologies fgrb,godg@belllabs.com Abstract. We address the problem of relating the result of model checking a partial state space of a system to the properties actually possessed by the system. We represent incomplete state spaces as partial Kripke structures, and give a 3valued interpretation to modal logic formulas on these structures. The third truth value ? means "unknown whether true or false". We define a preorder on partial Kripke structures that reflects their degree of completeness. We then provide a logical characterization of this preorder. This characterization thus relates properties of less complete structures to properties of more complete structures. We present similar results for labeled transition systems and show a connection to intuitionistic modal logic. We also present a 3valued CTL model checking algorithm, which returns ? only when the partial state space lacks information needed ...
Generalized Model Checking: Reasoning about Partial State Spaces
, 2000
"... We discuss the problem of model checking temporal properties on partial Kripke structures, which were used in [BG99] to represent incomplete state spaces. We first extend the results of [BG99] by showing that the modelchecking problem for any 3valued temporal logic can be reduced to two modelchec ..."
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Cited by 74 (6 self)
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We discuss the problem of model checking temporal properties on partial Kripke structures, which were used in [BG99] to represent incomplete state spaces. We first extend the results of [BG99] by showing that the modelchecking problem for any 3valued temporal logic can be reduced to two modelchecking problems for the corresponding 2valued temporal logic. We then introduce a new semantics for 3valued temporal logics that can give more definite answers than the previous one. With this semantics, the evaluation of a formula OE on a partial Kripke structure M returns the third truth value? (read "unknown") only if there exist Kripke structures M1 and M2 that both complete M and such that M1 satisfies OE while M2 violates OE, hence making the value of OE on M truly unknown. The partial Kripke structure M can thus be viewed as a partial solution to the satisfiability problem which reduces the solution space to complete Kripke structures that are more complete than M wit...
ManyValued Modal Logics II
 Fundamenta Informaticae
, 1992
"... Suppose there are several experts, with some dominating others (expert A dominates expert B if B says something is true whenever A says it is). Suppose, further, that each of the experts has his or her own view of what is possible  in other words each of the experts has their own Kripke model in ..."
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Cited by 22 (0 self)
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Suppose there are several experts, with some dominating others (expert A dominates expert B if B says something is true whenever A says it is). Suppose, further, that each of the experts has his or her own view of what is possible  in other words each of the experts has their own Kripke model in mind (subject, of course, to the dominance relation that may hold between experts). How will they assign truth values to sentences in a common modal language, and on what sentences will they agree? This problem can be reformulated as one about manyvalued Kripke models, allowing manyvalued accessibility relations. This is a natural generalization of conventional Kripke models that has only recently been looked at. The equivalence between the manyvalued version and the multiple expert one will be formally established. Finally we will axiomatize manyvalued modal logics, and sketch a proof of completeness.
A domain equation for refinement of partial systems
 UNDER CONSIDERATION FOR PUBLICATION IN MATH. STRUCT. IN COMP. SCIENC
"... ..."
Model Checking with MultiValued Logics
 In ICALP
, 2003
"... In multivalued model checking, a temporal logic formula is interpreted relative to a structure not as a truth value but as an element of a lattice. Applications of multivalued model checking include abstraction techniques, temporal logic query checking, and the analysis of conflict in multivi ..."
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In multivalued model checking, a temporal logic formula is interpreted relative to a structure not as a truth value but as an element of a lattice. Applications of multivalued model checking include abstraction techniques, temporal logic query checking, and the analysis of conflict in multiview specifications. In this paper we simplify and extend existing work on algorithms for multivalued model checking. We show how to reduce multivalued model checking with any distributive DeMorgan lattice to standard, twovalued model checking. From this reduction we derive complexity bounds for multivalued model checking for various temporal logics. We also present a direct, automatatheoretic algorithm for multivalued model checking with logics as expressive as the modal mucalculus. As part of showing the correctness of this algorithm, we present new, basic results about extended alternating automata, a generalization of standard alternating automata.
ManyValued Modal Logics II Melvin
, 2004
"... Suppose there are several experts, with some dominating others (expert A dominates expert B if B says something is true whenever A says it is). Suppose, further, that each of the experts has his or her own view of what is possible — in other words each of the experts has their own Kripke model in mi ..."
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Suppose there are several experts, with some dominating others (expert A dominates expert B if B says something is true whenever A says it is). Suppose, further, that each of the experts has his or her own view of what is possible — in other words each of the experts has their own Kripke model in mind (subject, of course, to the dominance relation that may hold between experts). How will they assign truth values to sentences in a common modal language, and on what sentences will they agree? This problem can be reformulated as one about manyvalued Kripke models, allowing manyvalued accessibility relations. This is a natural generalization of conventional Kripke models that has only recently been looked at. The equivalence between the manyvalued version and the multiple expert one will be formally established. Finally we will axiomatize manyvalued modal logics, and sketch a proof of completeness. 1