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Automating FirstOrder Relational Logic
, 2000
"... An analysis is described that can automatically find models of firstorder formulas with relational operators and scalar quantifiers. The formula is translated to a quantifierfree boolean formula that has a model exactly when the original formula has a model within a given scope (that is, involving ..."
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Cited by 143 (23 self)
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An analysis is described that can automatically find models of firstorder formulas with relational operators and scalar quantifiers. The formula is translated to a quantifierfree boolean formula that has a model exactly when the original formula has a model within a given scope (that is
Computing With FirstOrder Logic
, 1995
"... We study two important extensions of firstorder logic (FO) with iteration, the fixpoint and while queries. The main result of the paper concerns the open problem of the relationship between fixpoint and while: they are the same iff ptime = pspace. These and other expressibility results are obtaine ..."
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Cited by 55 (13 self)
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We study two important extensions of firstorder logic (FO) with iteration, the fixpoint and while queries. The main result of the paper concerns the open problem of the relationship between fixpoint and while: they are the same iff ptime = pspace. These and other expressibility results
The logic of constraint satisfaction
, 1992
"... The constraint satisfaction problem (CSP) formalization has been a productive tool within Artificial Intelligence and related areas. The finite CSP (FCSP) framework is presented here as a restricted logical calculus within a space of logical representation and reasoning systems. FCSP is formulated i ..."
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Cited by 265 (5 self)
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in a variety of logical settings: theorem proving in first order predicate calculus, propositional theorem proving (and hence SAT), the Prolog and Datalog approaches, constraint network algorithms, a logical interpreter for networks of constraints, the constraint logic programming (CLP) paradigm
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 273 (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
On the Decision Problem for TwoVariable FirstOrder Logic
, 1997
"... We identify the computational complexity of the satisfiability problem for FO², the fragment of firstorder logic consisting of all relational firstorder sentences with at most two distinct variables. Although this fragment was shown to be decidable a long time ago, the computational complexity ..."
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Cited by 83 (1 self)
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We identify the computational complexity of the satisfiability problem for FO², the fragment of firstorder logic consisting of all relational firstorder sentences with at most two distinct variables. Although this fragment was shown to be decidable a long time ago, the computational complexity
Approximate reasoning in firstorder logic theories
"... Many computational settings are concerned with finding (all) models of a firstorder logic theory for a fixed, finite domain. In this paper, we present a method to compute from a given theory and finite domain an approximate structure: a structure that approximates all models. We show confluence of ..."
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Cited by 2 (2 self)
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Many computational settings are concerned with finding (all) models of a firstorder logic theory for a fixed, finite domain. In this paper, we present a method to compute from a given theory and finite domain an approximate structure: a structure that approximates all models. We show confluence
Lindström theorems for fragments of firstorder logic
, 2007
"... Lindström theorems characterize logics in terms of modeltheoretic conditions such as Compactness and the LöwenheimSkolem property. Most existing characterizations of this kind concern extensions of firstorder logic. But on the other hand, many logics relevant to computer science are fragments o ..."
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Cited by 12 (3 self)
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Lindström theorems characterize logics in terms of modeltheoretic conditions such as Compactness and the LöwenheimSkolem property. Most existing characterizations of this kind concern extensions of firstorder logic. But on the other hand, many logics relevant to computer science are fragments
A PROOF OF COMPLETENESS FOR CONTINUOUS FIRSTORDER LOGIC
, 2009
"... Continuous firstorder logic has found interest among model theorists who wish to extend the classical analysis of “algebraic” structures (such as fields, group, and graphs) to various natural classes of complete metric structures (such as probability algebras, Hilbert spaces, and Banach spaces). W ..."
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Cited by 8 (1 self)
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). With research in continuous firstorder logic preoccupied with studying the model theory of this framework, we find a natural question calls for attention: Is there an interesting set of axioms yielding a completeness result? The primary purpose of this article is to show that a certain, interesting set
A DavisPutnam Program and its Application to Finite FirstOrder Model Search: Quasigroup Existence Problems
, 1994
"... This document describes the implementation and use of a DavisPutnam procedure for the propositional satisfiability problem. It also describes code that takes statements in firstorder logic with equality and a domain size n searches for models of size n. The firstorder modelsearching code transfor ..."
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Cited by 107 (10 self)
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This document describes the implementation and use of a DavisPutnam procedure for the propositional satisfiability problem. It also describes code that takes statements in firstorder logic with equality and a domain size n searches for models of size n. The firstorder modelsearching code
On the Translation of HigherOrder Problems into FirstOrder Logic
 Proceedings of ECAI94
, 1994
"... . In most cases higherorder logic is based on the  calculus in order to avoid the infinite set of socalled comprehension axioms. However, there is a price to be paid, namely an undecidable unification algorithm. If we do not use the calculus, but translate higherorder expressions into firstor ..."
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Cited by 8 (4 self)
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Henkinstyle general model semantics. 1 Introduction Firstorder logic is a powerful tool for ...
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