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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 ..."
Abstract

Cited by 218 (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...
P.: Generalized model checking: Reasoning about partial state spaces. In: CONCUR’00
, 2000
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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
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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
DOI: 10.1017/S0960129504004268 Printed in the United Kingdom A domain equation for refinement of partial systems
, 2002
"... A reactive system can be specified by a labelled transition system, which indicates static structure, along with temporallogic formulas, which assert dynamic behaviour. But refining the former while preserving the latter can be difficult, because: (i) Labelled transition systems are ‘total ’ – cha ..."
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A reactive system can be specified by a labelled transition system, which indicates static structure, along with temporallogic formulas, which assert dynamic behaviour. But refining the former while preserving the latter can be difficult, because: (i) Labelled transition systems are ‘total ’ – characterised up to bisimulation – meaning that no new transition structure can appear in a refinement. (ii) Alternatively, a refinement criterion not based on bisimulation might generate a refined transition system that violates the temporal properties. In response, Larsen and Thomson proposed modal transition systems, which are ‘partial’, and defined a refinement criterion that preserved formulas in Hennessy–Milner logic. We show that modal transition systems are, up to a saturation condition, exactly the mixed transition systems of Dams that meet a mix condition, and we extend such systems to nonflat state sets. We then solve a domain equation over the mixed powerdomain whose solution is a bifinite domain that is universal for all saturated modal transition systems and is itself fully abstract when considered as a modal transition system. We demonstrate that many frameworks of partial systems can be translated into the domain: partial Kripke structures, partial bisimulation structures, Kripke modal transition systems, and pointershapeanalysis graphs. 1.