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42
Formalizing action and change in modal logic I: the frame problem
, 1999
"... We present the basic framework of a logic of actions and plans defined in terms of modal logic combined with a notion of dependence. The latter is used as a weak causal connection between actions and literals. In this paper we focus on the frame problem and demonstrate how it can be solved in our fr ..."
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Cited by 58 (15 self)
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We present the basic framework of a logic of actions and plans defined in terms of modal logic combined with a notion of dependence. The latter is used as a weak causal connection between actions and literals. In this paper we focus on the frame problem and demonstrate how it can be solved in our framework in a simple and monotonic way. We give the semantics, and associate an axiomatics and a decision procedure to it. The decision procedure is based on a sound and complete tableau method with single step rules to treat dependence. We show how it can be used to generate plans. Our solution is formally assessed by a translation of Gelfond and Lifschitz' logic A. We briefly sketch the second part of the paper, showing how we can go beyond A by some examples involving nondeterminism and ramifications.
Completeness and Herbrand Theorems for Nominal Logic
 Journal of Symbolic Logic
, 2006
"... Nominal logic is a variant of firstorder logic in which abstract syntax with names and binding is formalized in terms of two basic operations: nameswapping and freshness. It relies on two important principles: equivariance (validity is preserved by nameswapping), and fresh name generation (&qu ..."
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Cited by 25 (5 self)
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Nominal logic is a variant of firstorder logic in which abstract syntax with names and binding is formalized in terms of two basic operations: nameswapping and freshness. It relies on two important principles: equivariance (validity is preserved by nameswapping), and fresh name generation ("new" or fresh names can always be chosen).
A mechanically verified, sound and complete theorem prover for first order logic
 In Theorem Proving in Higher Order Logics, 18th International Conference, TPHOLs 2005, volume 3603 of Lecture Notes in Computer Science
, 2005
"... Abstract. We present a system of first order logic, together with soundness and completeness proofs wrt. standard first order semantics. Proofs are mechanised in Isabelle/HOL. Our definitions are computable, allowing us to derive an algorithm to test for first order validity. This algorithm may be e ..."
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Cited by 17 (0 self)
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Abstract. We present a system of first order logic, together with soundness and completeness proofs wrt. standard first order semantics. Proofs are mechanised in Isabelle/HOL. Our definitions are computable, allowing us to derive an algorithm to test for first order validity. This algorithm may be executed in Isabelle/HOL using the rewrite engine. Alternatively the algorithm has been ported to OCaML. 1
Erdős Graphs Resolve Fine's Canonicity Problem
 THE BULLETIN OF SYMBOLIC LOGIC
, 2003
"... We show that there exist 2^ℵ0 equational classes of Boolean algebras with operators that are not generated by the complex algebras of any firstorder definable class of relational structures. Using a variant of this construction, we resolve a longstanding question of Fine, by exhibiting ..."
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Cited by 15 (8 self)
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We show that there exist 2^&alefsym;0 equational classes of Boolean algebras with operators that are not generated by the complex algebras of any firstorder definable class of relational structures. Using a variant of this construction, we resolve a longstanding question of Fine, by exhibiting a bimodal logic that is valid in its canonical frames, but is not sound and complete for any firstorder definable class of Kripke frames. The constructions use the result of Erdős that there are finite graphs with arbitrarily large chromatic number and girth.
The Mathematical Development Of Set Theory  From Cantor To Cohen
 The Bulletin of Symbolic Logic
, 1996
"... This article is dedicated to Professor Burton Dreben on his coming of age. I owe him particular thanks for his careful reading and numerous suggestions for improvement. My thanks go also to Jose Ruiz and the referee for their helpful comments. Parts of this account were given at the 1995 summer meet ..."
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Cited by 11 (2 self)
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This article is dedicated to Professor Burton Dreben on his coming of age. I owe him particular thanks for his careful reading and numerous suggestions for improvement. My thanks go also to Jose Ruiz and the referee for their helpful comments. Parts of this account were given at the 1995 summer meeting of the Association for Symbolic Logic at Haifa, in the Massachusetts Institute of Technology logic seminar, and to the Paris Logic Group. The author would like to express his thanks to the various organizers, as well as his gratitude to the Hebrew University of Jerusalem for its hospitality during the preparation of this article in the autumn of 1995.
A History of Satisfiability
, 2009
"... 1.1. Preface: the concept of satisfiability Interest in Satisfiability is expanding for a variety of reasons, not in the least because nowadays more problems are being solved faster by SAT solvers than other means. This is probably because Satisfiability stands at the crossroads of logic, graph theo ..."
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Cited by 7 (0 self)
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1.1. Preface: the concept of satisfiability Interest in Satisfiability is expanding for a variety of reasons, not in the least because nowadays more problems are being solved faster by SAT solvers than other means. This is probably because Satisfiability stands at the crossroads of logic, graph theory, computer science, computer engineering, and operations research. Thus, many problems originating in one of these fields typically have multiple translations to Satisfiability and there exist many mathematical tools available to the SAT solver to assist in solving them with improved performance. Because of the strong links to so many fields, especially logic, the history of Satisfiability can best be understood as it unfolds with respect to its logic roots. Thus, in addition to timelining events specific to Satisfiability, the chapter follows the presence of Satisfiability in logic as it was developed to model human thought and scientific reasoning through its use in computer design and now as modeling tool for solving a variety of practical problems. In order to succeed in this, we must introduce many ideas that have arisen during numerous attempts to reason