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Temporal and modal logic
 HANDBOOK OF THEORETICAL COMPUTER SCIENCE
, 1995
"... We give a comprehensive and unifying survey of the theoretical aspects of Temporal and modal logic. ..."
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Cited by 1300 (17 self)
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We give a comprehensive and unifying survey of the theoretical aspects of Temporal and modal logic.
The Foundation of a Generic Theorem Prover
 Journal of Automated Reasoning
, 1989
"... Isabelle [28, 30] is an interactive theorem prover that supports a variety of logics. It represents rules as propositions (not as functions) and builds proofs by combining rules. These operations constitute a metalogic (or `logical framework') in which the objectlogics are formalized. Isabell ..."
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Cited by 471 (49 self)
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. Isabelle is now based on higherorder logic  a precise and wellunderstood foundation. Examples illustrate use of this metalogic to formalize logics and proofs. Axioms for firstorder logic are shown sound and complete. Backwards proof is formalized by metareasoning about objectlevel entailment
Implementing and Evaluating Provers for Firstorder Modal Logics
"... Abstract. While there is a broad literature on the theory of firstorder modal logics, little is known about practical reasoning systems for them. This paper presents several implementations of fully automated theorem provers for firstorder modal logics based on different proof calculi. Among these ..."
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Cited by 8 (5 self)
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Abstract. While there is a broad literature on the theory of firstorder modal logics, little is known about practical reasoning systems for them. This paper presents several implementations of fully automated theorem provers for firstorder modal logics based on different proof calculi. Among
HOL based firstorder modal logic provers
 Proceedings of the 19th International Conference on Logic for Programming, Artificial Intelligence and Reasoning (LPAR), volume 8312 of LNCS
, 2013
"... Abstract. Firstorder modal logics (FMLs) can be modeled as natural fragments of classical higherorder logic (HOL). The FMLtoHOL tool exploits this fact and it enables the application of offtheshelf HOL provers and model finders for reasoning within FMLs. The tool bridges between the qmfsyntax ..."
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Cited by 3 (2 self)
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Abstract. Firstorder modal logics (FMLs) can be modeled as natural fragments of classical higherorder logic (HOL). The FMLtoHOL tool exploits this fact and it enables the application of offtheshelf HOL provers and model finders for reasoning within FMLs. The tool bridges between the qmf
An Analysis of FirstOrder Logics of Probability
 Artificial Intelligence
, 1990
"... : We consider two approaches to giving semantics to firstorder logics of probability. The first approach puts a probability on the domain, and is appropriate for giving semantics to formulas involving statistical information such as "The probability that a randomly chosen bird flies is greater ..."
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Cited by 316 (18 self)
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: We consider two approaches to giving semantics to firstorder logics of probability. The first approach puts a probability on the domain, and is appropriate for giving semantics to formulas involving statistical information such as "The probability that a randomly chosen bird flies
The Semantics of Predicate Logic as a Programming Language
 Journal of the ACM
, 1976
"... ABSTRACT Sentences in firstorder predicate logic can be usefully interpreted as programs In this paper the operational and fixpomt semantics of predicate logic programs are defined, and the connections with the proof theory and model theory of logic are investigated It is concluded that operational ..."
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Cited by 810 (18 self)
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ABSTRACT Sentences in firstorder predicate logic can be usefully interpreted as programs In this paper the operational and fixpomt semantics of predicate logic programs are defined, and the connections with the proof theory and model theory of logic are investigated It is concluded
Implementing Connection Calculi for Firstorder Modal Logics
 9th International Workshop on the Implementation of Logics, Merida/Venezuela
, 2012
"... This paper presents an implementation of an automated theorem prover for firstorder modal logic that works for the constant, cumulative, and varying domain of the modal logics D, T, S4, and S5. It is based on the connection calculus for classical logic and uses prefixes representing world paths and ..."
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Cited by 4 (3 self)
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This paper presents an implementation of an automated theorem prover for firstorder modal logic that works for the constant, cumulative, and varying domain of the modal logics D, T, S4, and S5. It is based on the connection calculus for classical logic and uses prefixes representing world paths
A Framework for Defining Logics
 JOURNAL OF THE ASSOCIATION FOR COMPUTING MACHINERY
, 1993
"... The Edinburgh Logical Framework (LF) provides a means to define (or present) logics. It is based on a general treatment of syntax, rules, and proofs by means of a typed calculus with dependent types. Syntax is treated in a style similar to, but more general than, MartinLof's system of ariti ..."
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Cited by 807 (45 self)
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conditions and leads to a uniform treatment of rules and proofs whereby rules are viewed as proofs of higherorder judgements and proof checking is reduced to type checking. The practical benefit of our treatment of formal systems is that logicindependent tools such as proof editors and proof checkers
Automatic verification of finitestate concurrent systems using temporal logic specifications
 ACM Transactions on Programming Languages and Systems
, 1986
"... We give an efficient procedure for verifying that a finitestate concurrent system meets a specification expressed in a (propositional, branchingtime) temporal logic. Our algorithm has complexity linear in both the size of the specification and the size of the global state graph for the concurrent ..."
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Cited by 1384 (62 self)
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We give an efficient procedure for verifying that a finitestate concurrent system meets a specification expressed in a (propositional, branchingtime) temporal logic. Our algorithm has complexity linear in both the size of the specification and the size of the global state graph for the concurrent
Abduction in Logic Programming
"... Abduction in Logic Programming started in the late 80s, early 90s, in an attempt to extend logic programming into a framework suitable for a variety of problems in Artificial Intelligence and other areas of Computer Science. This paper aims to chart out the main developments of the field over th ..."
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Cited by 616 (76 self)
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Abduction in Logic Programming started in the late 80s, early 90s, in an attempt to extend logic programming into a framework suitable for a variety of problems in Artificial Intelligence and other areas of Computer Science. This paper aims to chart out the main developments of the field over
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