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Parametric Shape Analysis via 3Valued Logic
, 2001
"... Shape Analysis concerns the problem of determining "shape invariants"... ..."
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Cited by 654 (80 self)
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Shape Analysis concerns the problem of determining "shape invariants"...
Rough Sets and 3Valued Logics
, 2008
"... In the paper we explore the idea of describing Pawlak’s rough sets using threevalued logic, whereby the value t corresponds to the positive region of a set, the value f — to the negative region, and the undefined value u — to the border of the set. Due to the properties of the above regions in rou ..."
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in rough set theory, the semantics of the logic is described using a nondeterministic matrix (Nmatrix). With the strong semantics, where only the value t is treated as designated, the above logic is a “common denominator” for Kleene and Łukasiewicz 3valued logics, which represent its two different
Static Program Analysis via 3Valued Logic
, 2004
"... This paper reviews the principles behind the paradigm of "abstract interpretation via 3valued logic," discusses recent work to extend the approach, and summarizes ongoing research aimed at overcoming remaining limitations on the ability to create programanalysis algorithms fully automa ..."
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Cited by 26 (3 self)
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This paper reviews the principles behind the paradigm of "abstract interpretation via 3valued logic," discusses recent work to extend the approach, and summarizes ongoing research aimed at overcoming remaining limitations on the ability to create programanalysis algorithms fully
Natural 3valued logics—characterization and proof theory
 J. of Symbolic Logic
, 1991
"... Manyvalued logics in general and 3valued logic in particular is an old subject which had its beginning in the work of Lukasiewicz [Luk]. Recently there is a revived interest in this topic, both for its own sake (see, e.g. [Ho]), and also because of its potential applications in several areas of co ..."
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Cited by 12 (0 self)
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Manyvalued logics in general and 3valued logic in particular is an old subject which had its beginning in the work of Lukasiewicz [Luk]. Recently there is a revived interest in this topic, both for its own sake (see, e.g. [Ho]), and also because of its potential applications in several areas
On the First Degree Entailment of Two 3Valued Logics
"... We note first that the first degree entailment of / Lukasiewicz's 3valued logic and a 3valued logic that is extracted of Belnap's 4valued logic is the same. Then, we give an axiomatization of that entailment as the calculus E fde +A:A!B :B , where E fde is the first degree entailment ..."
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We note first that the first degree entailment of / Lukasiewicz's 3valued logic and a 3valued logic that is extracted of Belnap's 4valued logic is the same. Then, we give an axiomatization of that entailment as the calculus E fde +A:A!B :B , where E fde is the first degree
WellFounded Inference and 3Valued Logics
, 1998
"... We define a simple logical semantics based on minimal models in / Lukasiewicz's 3valued logic, / L 3 . On normal logic programs it is equivalent to the wellfounded semantics (WFS), and on disjunctive programs it is equivalent to the Pstable semantics of Eiter, Leone and Sacc`a, hence to Przy ..."
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We define a simple logical semantics based on minimal models in / Lukasiewicz's 3valued logic, / L 3 . On normal logic programs it is equivalent to the wellfounded semantics (WFS), and on disjunctive programs it is equivalent to the Pstable semantics of Eiter, Leone and Sacc`a, hence
Abstraction Refinement for 3ValuedLogic Analysis
, 2004
"... This paper concerns the question of how to create abstractions that are useful for program analysis. It presents a method that refines an abstraction automatically for analysis problems in which the semantics of statements and the query of interest are expressed using logical formulas. Refinement ..."
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Cited by 6 (2 self)
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This paper concerns the question of how to create abstractions that are useful for program analysis. It presents a method that refines an abstraction automatically for analysis problems in which the semantics of statements and the query of interest are expressed using logical formulas
Lightweight specialized 3valued logic shape analyzer
 EECS Department, University of California, Berkeley
"... personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires pri ..."
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Cited by 1 (1 self)
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personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission. Acknowledgement I thank Mooly Sagiv and Roman Manevich for their useful feedback and continuous advice. I thank Ras Bodik for supporting my work on this research.
Implementing a 3Valued Logic in Coq
"... In the world of expressions, undefined values arise quite naturally. Simple examples are: the result of division by zero, or the integer square root of a negative number. When manipulating specifications in the form of mathematical expressions, possibly undefined expressions cannot be ignored. Rathe ..."
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. Rather, we choose to address the problem. This paper describes how the Coq theorem prover was used to implement a threevalued logic, where the three values are True, False and the undefined logical value ?. The threevalued logic is based on an extended propositional logic, which uses nonstrict versions
ParametricShapeAnalysisvia3ValuedLogic
"... Wepresentafamilyofabstractinterpretationalgorithmsthat arecapableofdetermining\shapeinvariants"ofprograms thatperformdestructiveupdatingondynamicallyallocated storage.Themainideaistorepresentthestoresthatcanpossiblyariseduringexecutionusingthreevaluedlogicalstructures. Questionsaboutpropertie ..."
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.Themainideaistorepresentthestoresthatcanpossiblyariseduringexecutionusingthreevaluedlogicalstructures. Questionsaboutpropertiesofstorescanbeansweredby evaluatingpredicatelogicformulaeusingKleene'ssemantics ofthreevaluedlogic: Ifaformulaevaluatestotrue,thentheformulaholdsin everystorerepresentedbythethreevaluedstructure. Ifaformulaevaluatestofalse,thentheformuladoes notholdinanystorerepresentedbythethreevalued structure
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