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An Implementation of Narrowing Strategies
 Journal of the ACM
, 2001
"... This paper describes an implementation of narrowing, an essential component of implementations of modern functional logic languages. These implementations rely on narrowing, in particular on some optimal narrowing strategies, to execute functional logic programs. We translate functional logic progra ..."
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Cited by 294 (123 self)
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This paper describes an implementation of narrowing, an essential component of implementations of modern functional logic languages. These implementations rely on narrowing, in particular on some optimal narrowing strategies, to execute functional logic programs. We translate functional logic programs into imperative (Java) programs without an intermediate abstract machine. A central idea of our approach is the explicit representation and processing of narrowing computations as data objects. This enables the implementation of operationally complete strategies (i.e., without backtracking) or techniques for search control (e.g., encapsulated search). Thanks to the use of an intermediate and portable representation of programs, our implementation is general enough to be used as a common back end for a wide variety of functional logic languages.
Ramification and Causality
 Artificial Intelligence
, 1997
"... The ramification problem in the context of commonsense reasoning about actions and change names the challenge to accommodate actions whose execution causes indirect effects. Not being part of the respective action specification, such effects are consequences of general laws describing dependencies b ..."
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Cited by 149 (20 self)
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The ramification problem in the context of commonsense reasoning about actions and change names the challenge to accommodate actions whose execution causes indirect effects. Not being part of the respective action specification, such effects are consequences of general laws describing dependencies between components of the world description. We present a general approach to this problem which incorporates causality, formalized by directed relations between two single effects stating that, under specific circumstances, the occurrence of the first causes the second. Moreover, necessity of exploiting causal information in this way or a similar is argued by elaborating the limitations of common paradigms employed to handle ramifications, namely, the principle of categorization and the policy of minimal change. Our abstract solution is exemplarily integrated into a specific calculus based on the logic programming paradigm. To apper in: Artificial Intelligence Journal On leave from FG Inte...
Automated Deduction by Theory Resolution
 Journal of Automated Reasoning
, 1985
"... Theory resolution constitutes a set of complete procedures for incorporating theories into a resolution theoremproving program, thereby making it unnecessary to resolve directly upon axioms of the theory. This can greatly reduce the length of proofs and the size of the search space. Theory resoluti ..."
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Cited by 121 (1 self)
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Theory resolution constitutes a set of complete procedures for incorporating theories into a resolution theoremproving program, thereby making it unnecessary to resolve directly upon axioms of the theory. This can greatly reduce the length of proofs and the size of the search space. Theory resolution effects a beneficial division of labor, improving the performance of the theorem prover and increasing the applicability of the specialized reasoning procedures. Total theory resolution utilizes a decision procedure that is capable of determining unsatisfiability of any set of clauses using predicates in the theory. Partial theory resolution employs a weaker decision procedure that can determine potential unsatisfiability of sets of literals. Applications include the building in of both mathematical and special decision procedures, e.g., for the taxonomic information furnished by a knowledge representation system. Theory resolution is a generalization of numerous previously known resolution refinements. Its power is demonstrated by comparing solutions of "Schubert's Steamroller" challenge problem with and without building in axioms through theory resolution. 1 1
Higherorder Unification via Explicit Substitutions (Extended Abstract)
 Proceedings of LICS'95
, 1995
"... Higherorder unification is equational unification for βηconversion. But it is not firstorder equational unification, as substitution has to avoid capture. In this paper higherorder unification is reduced to firstorder equational unification in a suitable theory: the λσcal ..."
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Cited by 103 (13 self)
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Higherorder unification is equational unification for βηconversion. But it is not firstorder equational unification, as substitution has to avoid capture. In this paper higherorder unification is reduced to firstorder equational unification in a suitable theory: the λσcalculus of explicit substitutions.
Equations and rewrite rules: a survey
 In Formal Language Theory: Perspectives and Open Problems
, 1980
"... bY ..."
Theorem Proving Modulo
 Journal of Automated Reasoning
"... Abstract. Deduction modulo is a way to remove computational arguments from proofs by reasoning modulo a congruence on propositions. Such a technique, issued from automated theorem proving, is of much wider interest because it permits to separate computations and deductions in a clean way. The first ..."
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Cited by 75 (14 self)
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Abstract. Deduction modulo is a way to remove computational arguments from proofs by reasoning modulo a congruence on propositions. Such a technique, issued from automated theorem proving, is of much wider interest because it permits to separate computations and deductions in a clean way. The first contribution of this paper is to define a sequent calculus modulo that gives a proof theoretic account of the combination of computations and deductions. The congruence on propositions is handled via rewrite rules and equational axioms. Rewrite rules apply to terms and also directly to atomic propositions. The second contribution is to give a complete proof search method, called Extended Narrowing and Resolution (ENAR), for theorem proving modulo such congruences. The completeness of this method is proved with respect to provability in sequent calculus modulo. An important application is that higherorder logic can be presented as a theory modulo. Applying the Extended Narrowing and Resolution method to this presentation of higherorder logic subsumes full higherorder resolution.
Compiling and Verifying Security Protocols
, 2000
"... We propose a direct and fully automated translation from standard security protocol descriptions to rewrite rules. This compilation defines nonambiguous operational semantics for protocols and intruder behavior: they are rewrite systems executed by applying a variant of acnarrowing. The rewrite ru ..."
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Cited by 54 (6 self)
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We propose a direct and fully automated translation from standard security protocol descriptions to rewrite rules. This compilation defines nonambiguous operational semantics for protocols and intruder behavior: they are rewrite systems executed by applying a variant of acnarrowing. The rewrite rules are processed by the theoremprover daTac. Multiple instances of a protocol can be run simultaneously as well as a model of the intruder (among several possible). The existence of flaws in the protocol is revealed by the derivation of an inconsistency. Our implementation of the compiler CASRUL, together with the prover daTac, permitted us to derive security flaws in many classical cryptographic protocols.
The Substitutional Framework for Sorted Deduction: Fundamental Results on Hybrid Reasoning
 Artificial Intelligence
, 1990
"... Researchers in artificial intelligence have recently been taking great interest in hybrid representations, among them sorted logicslogics that link a traditional logical representation to a taxonomic (or sort) representation such as those prevalent in semantic networks. This paper introduces a ge ..."
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Cited by 50 (9 self)
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Researchers in artificial intelligence have recently been taking great interest in hybrid representations, among them sorted logicslogics that link a traditional logical representation to a taxonomic (or sort) representation such as those prevalent in semantic networks. This paper introduces a general frameworkthe substitutional frameworkfor integrating logical deduction and sortal deduction to form a deductive system for sorted logic. This paper also presents results that provide the theoretical underpinnings of the framework. A distinguishing characteristic of a deductive system that is structured according to the substitutional framework is that the sort subsystem is invoked only when the logic subsystem performs unification, and thus sort information is used only in determining what substitutions to make for variables. Unlike every other known approach to sorted deduction, the substitutional framework provides for a systematic transformation of unsorted deductive systems ...
Proof Normalization Modulo
, 1998
"... We consider a class of logical formalisms, in which firstorder logic is extended by identifying propositions modulo a given congruence. We particularly focus on the case where this congruence is induced by a confluent and terminating rewrite system over the propositions. This extension enhances the ..."
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Cited by 46 (17 self)
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We consider a class of logical formalisms, in which firstorder logic is extended by identifying propositions modulo a given congruence. We particularly focus on the case where this congruence is induced by a confluent and terminating rewrite system over the propositions. This extension enhances the power of firstorder logic and various formalisms, including higherorder logic, can be described in this framework. We conjecture that proof normalization and logical consistency always hold over this class of formalisms, provided some minimal conditions over the rewrite system are fulfilled. We prove this conjecture for some subcases, including higherorder logic. At last, we extend these results to classical sequent calculus.