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15
Fundamentals Of Deductive Program Synthesis
 IEEE Transactions on Software Engineering
, 1992
"... An informal tutorial is presented for program synthesis, with an emphasis on deductive methods. According to this approach, to construct a program meeting a given specification, we prove the existence of an object meeting the specified conditions. The proof is restricted to be sufficiently construct ..."
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Cited by 65 (1 self)
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An informal tutorial is presented for program synthesis, with an emphasis on deductive methods. According to this approach, to construct a program meeting a given specification, we prove the existence of an object meeting the specified conditions. The proof is restricted to be sufficiently constructive, in the sense that, in establishing the existence of the desired output, the proof is forced to indicate a computational method for finding it. That method becomes the basis for a program that can be extracted from the proof. The exposition is based on the deductivetableau system, a theoremproving framework particularly suitable for program synthesis. The system includes a nonclausal resolution rule, facilities for reasoning about equality, and a wellfounded induction rule. INTRODUCTION This is an introduction to program synthesis, the derivation of a program to meet a given specification. It focuses on the deductive approach, in which the derivation task is regarded as a problem of ...
Towards an optimal cnf encoding of boolean cardinality constraints
 In Proc. of the 11th Intl. Conf. on Principles and Practice of Constraint Programming (CP 2005
, 2005
"... Abstract. We consider the problem of encoding Boolean cardinality constraints in conjunctive normal form (CNF). Boolean cardinality constraints are formulae expressing that at most (resp. at least) k out of n propositional variables or formulae are true. We present a unifying framework for a whole f ..."
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Cited by 37 (1 self)
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Abstract. We consider the problem of encoding Boolean cardinality constraints in conjunctive normal form (CNF). Boolean cardinality constraints are formulae expressing that at most (resp. at least) k out of n propositional variables or formulae are true. We present a unifying framework for a whole family of such encodings encompassing previously proposed solutions. We give two novel encodings that improve upon existing results, one which requires only 7n clauses and 2n additional variables, and another one demanding O(n · k) clauses, but with the advantage that inconsistencies can be detected in linear time by unit propagation alone. Moreover, we prove a linear lower bound on the number of required clauses for any such encoding. 1
Exploiting Data Dependencies in ManyValued Logics
 Journal of Applied NonClassical Logics
, 1996
"... . The purpose of this paper is to make some practically relevant results in automated theorem proving available to manyvalued logics with suitable modifications. We are working with a notion of manyvalued firstorder clauses which any finitelyvalued logic formula can be translated into and that h ..."
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Cited by 21 (7 self)
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. The purpose of this paper is to make some practically relevant results in automated theorem proving available to manyvalued logics with suitable modifications. We are working with a notion of manyvalued firstorder clauses which any finitelyvalued logic formula can be translated into and that has been used several times in the literature, but in an ad hoc way. We give a manyvalued version of polarity which in turn leads to natural manyvalued counterparts of Horn formulas, hyperresolution, and a DavisPutnam procedure. We show that the manyvalued generalizations share many of the desirable properties of the classical versions. Our results justify and generalize several earlier results on theorem proving in manyvalued logics. KEYWORDS: manyvalued logic, polarity, Horn formula, direct products of structures, resolution, DavisPutnam procedure Introduction The purpose of this paper is to make some practically relevant results in automated theorem proving available to manyvalue...
Interest driven suppositional reasoning
 Journal of Automated Reasoning
, 1990
"... Abstract. The aim of this paper is to investigate two related aspects of human reasoning, and use the results to construct an automated theorem prover for the predicate calculus that at least approximately models human reasoning. The result is a nonresolution theorem prover that does not use Skolem ..."
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Cited by 11 (3 self)
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Abstract. The aim of this paper is to investigate two related aspects of human reasoning, and use the results to construct an automated theorem prover for the predicate calculus that at least approximately models human reasoning. The result is a nonresolution theorem prover that does not use Skolemization. It involves two central ideas. One is the interest constraints that are of central importance in guiding human reasoning. The other is the notion of suppositional reasoning, wherein one makes a supposition, draws inferences that depend upon that supposition, and then infers a conclusion that does not depend upon it. Suppositional reasoning is involved in the use of conditionals and reductio ad absurdum, and is central to human reasoning with quantifiers. The resulting theorem prover turns out to be surprisingly efficient, beating most resolution theorem provers on some hard problems.
Superposition with Equivalence Reasoning and Delayed Clause Normal Form Transformation
 Inf. Comput
, 2003
"... This paper describes a superposition calculus where quantifiers are eliminated lazily. Superposition and simplification inferences may employ equivalences that have arbitrary formulas at their smaller side. A closely related calculus is implemented in the Saturate system and has shown useful on many ..."
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Cited by 11 (0 self)
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This paper describes a superposition calculus where quantifiers are eliminated lazily. Superposition and simplification inferences may employ equivalences that have arbitrary formulas at their smaller side. A closely related calculus is implemented in the Saturate system and has shown useful on many examples, in particular in set theory. The paper presents a completeness proof and reports on practical experience obtained with the Saturate system.
A GraphBased Approach To Resolution In Temporal Logic
 In Temporal Logic, First International Conference, ICTL '94, Proceedings
, 1994
"... . In this paper, we present algorithms developed in order to implement a clausal resolution method for discrete, linear temporal logics, presented in [Fis91]. As part of this method, temporal formulae are rewritten into a normal form and both `nontemporal' and `temporal' inference rules are applied ..."
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Cited by 4 (3 self)
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. In this paper, we present algorithms developed in order to implement a clausal resolution method for discrete, linear temporal logics, presented in [Fis91]. As part of this method, temporal formulae are rewritten into a normal form and both `nontemporal' and `temporal' inference rules are applied. Through the use of a graphbased representation for the normal form, "efficient" search algorithms can be applied to detect sets of formulae for which temporal resolution is applicable. Further, rather than constructing the full graph structure, our algorithms only explore and construct as little of the graph as possible. These algorithms have been implemented and have been combined with subprograms performing translation to normal form and nontemporal resolution to produce an integrated resolution based temporal theoremprover. 1 Introduction Although resolution has been widely used as a decision procedure in classical logics, decision procedures in temporal logic have usually been tab...
A Unifying Framework for ALP, CLP and SQO
, 1996
"... This paper presents the TPCALP framework, a theoremproving approach which aims to unify Abductive Logic Programming (ALP), Constraint Logic Programming (CLP) and Semantic Query Optimization (SQO). The framework combines the use of definitions, as in ordinary logic programming, with the use of integ ..."
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Cited by 3 (1 self)
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This paper presents the TPCALP framework, a theoremproving approach which aims to unify Abductive Logic Programming (ALP), Constraint Logic Programming (CLP) and Semantic Query Optimization (SQO). The framework combines the use of definitions, as in ordinary logic programming, with the use of integrity constraints, as in ALP and SQO. The programmer can choose to represent knowledge in either form subject to the condition that the integrity constraints be "properties" of the definitions. The paper defines a proof procedure for the framework and presents some formal results for the proof procedure with respect to the framework semantics. The proof procedure executes definitions in conventional logic programming goal reduction manner, and integrity constraints in forward reasoning style to check potential answers for consistency. The integrity constraints are used to process goals when the definitions cannot be used, either because they are not accessible (as in ALP and SQO) or because t...
FirstOrder Polynomial Based Theorem Proving
, 1999
"... Introduction The Boolean ring or firstorder polynomial based theorem proving began with the work of Hsiang (1982, 1985). Hsiang extended the idea of using Boolean polynomials to represent propositional formulae to the case of firstorder predicate calculus. Based on the completion procedure of Knu ..."
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Cited by 2 (0 self)
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Introduction The Boolean ring or firstorder polynomial based theorem proving began with the work of Hsiang (1982, 1985). Hsiang extended the idea of using Boolean polynomials to represent propositional formulae to the case of firstorder predicate calculus. Based on the completion procedure of Knuth and Bendix (1970), the Nstrategy was proposed. Later on, by imitating the framework of Buchberger 's algorithm to compute the Grobner bases of polynomial ideals (Buchberger 1985), Kapur and Narendran (1985) developed another approach which is also referred to as the Grobner basis method. One obvious advantage of using Boolean polynomials is that every propositional formula has a unique representation, and sometimes it is easy to be generalized to some nonclassical logic systems (Chazarain et al. 1991; Wu and Tan 1994). Stimulated by them, some approaches and results have been reported (Bachmair and Dershowitz 1987; Dietrich 1986; Kapur and Zhang 1989; Wu and Liu 1998; Zhang 198
TheoremProving for Discrete Temporal Logic
, 1998
"... This chapter considers theorem proving for discrete temporal logics. We are interested in deciding or at least enumerating the formulas of the logic which are valid, that is, are true in all circumstances. Most of the techniques for temporal theoremproving have been extensions for methods developed ..."
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Cited by 1 (0 self)
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This chapter considers theorem proving for discrete temporal logics. We are interested in deciding or at least enumerating the formulas of the logic which are valid, that is, are true in all circumstances. Most of the techniques for temporal theoremproving have been extensions for methods developed for classical logics but completely novel techniques have also been developed. Initially we concentrate on discrete lineartime temporal logics, describing axiomatic, tableau, automata and resolution based approaches. The application of these approaches to other temporal logics is discussed. 1 Introduction Readers of this handbook will be aware of the wide variety of useful tasks which require reasoning about time. There are many applications of temporal reasoning tasks to problems of knowledge changing, to planning, to processing natural language, to managing the interchange of information, and to developing complex systems. There are a wide variety of temporal logics available in which s...