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104
Prolegomena to Logic Programming for NonMonotonic Reasoning
"... The present prolegomena consist, as all indeed do, in a critical discussion serving to introduce and interpret the extended works that follow in this book. As a result, the book is not a mere collection of excellent papers in their own specialty, but provides also the basics of the motivation, b ..."
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Cited by 22 (16 self)
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The present prolegomena consist, as all indeed do, in a critical discussion serving to introduce and interpret the extended works that follow in this book. As a result, the book is not a mere collection of excellent papers in their own specialty, but provides also the basics of the motivation, background history, important themes, bridges to other areas, and a common technical platform of the principal formalisms and approaches, augmented with examples. In the
A Flexible (C)LPBased Approach to the Analysis of ObjectOriented Programs
 In 17th International Symposium on Logicbased Program Synthesis and Transformation (LOPSTR’07
, 2007
"... Abstract. Static analyses of objectoriented programs usually rely on intermediate representations that respect the original semantics while having a more uniform and basic syntax. Most of the work involving objectoriented languages and abstract interpretation usually omits the description of that ..."
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Cited by 20 (7 self)
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Abstract. Static analyses of objectoriented programs usually rely on intermediate representations that respect the original semantics while having a more uniform and basic syntax. Most of the work involving objectoriented languages and abstract interpretation usually omits the description of that language or just refers to the Control Flow Graph (CFG) it represents. However, this lack of formalization on one hand results in an absence of assurances regarding the correctness of the transformation and on the other it typically strongly couples the analysis to the source language. In this work we present a framework for analysis of objectoriented languages in which in a first phase we transform the input program into a representation based on Horn clauses. This allows on one hand proving the transformation correct attending to a simple condition and on the other being able to apply an existing analyzer for (constraint) logic programming to automatically derive a safe approximation of the semantics of the original program. The approach is flexible in the sense that the first phase decouples the analyzer from most languagedependent features, and correct because the set of Horn clauses returned by the transformation phase safely approximates the standard semantics of the input program. The resulting analysis is also reasonably scalable due to the use of mature, modular (C)LPbased analyzers. The overall approach allows us to report results for mediumsized programs. 1
Deduction Systems Based on Resolution
, 1991
"... A general theory of deduction systems is presented. The theory is illustrated with deduction systems based on the resolution calculus, in particular with clause graphs. This theory distinguishes four constituents of a deduction system: ffl the logic, which establishes a notion of semantic entailmen ..."
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Cited by 19 (0 self)
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A general theory of deduction systems is presented. The theory is illustrated with deduction systems based on the resolution calculus, in particular with clause graphs. This theory distinguishes four constituents of a deduction system: ffl the logic, which establishes a notion of semantic entailment; ffl the calculus, whose rules of inference provide the syntactic counterpart of entailment; ffl the logical state transition system, which determines the representation of formulae or sets of formulae together with their interrelationships, and also may allow additional operations reducing the search space; ffl the control, which comprises the criteria used to choose the most promising from among all applicable inference steps. Much of the standard material on resolution is presented in this framework. For the last two levels many alternatives are discussed. Appropriately adjusted notions of soundness, completeness, confluence, and Noetherianness are introduced in order to characterize...
Investigating a general hierarchy of polynomially decidable classes of CNF's based on short treelike resolution proofs
, 1999
"... We investigate a hierarchy Gk (U ; S) of classes of conjunctive normal forms, recognizable and SATdecidable in polynomial time, with special emphasize on the corresponding hardness parameter hU ;S (F ) for clausesets F (the first level of inclusion). At level 0 an (incomplete, polytime) oracl ..."
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Cited by 16 (10 self)
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We investigate a hierarchy Gk (U ; S) of classes of conjunctive normal forms, recognizable and SATdecidable in polynomial time, with special emphasize on the corresponding hardness parameter hU ;S (F ) for clausesets F (the first level of inclusion). At level 0 an (incomplete, polytime) oracle U for unsatisfiability detection and an oracle S for satisfiability detection is used. The hierarchy from [Pretolani 96] is improved in this way with respect to strengthened satisfiability handling, simplified recognition and consistent relativization. Also a hierarchy of canonical polytime reductions with Unitclause propagation at the first level is obtained. General methods for upper and lower bounds on hU ;S (F ) are developed and applied to a number of wellknown examples. hU ;S (F ) admits several different characterizations, including the space complexity of treelike resolution and the use of pebble games as in [Esteban, Tor'an 99]. Using for S the class of linearly sat...
Linear tabulated resolution based on Prolog control strategy
, 2000
"... Infinite loops and redundant computations are long recognized open problems in Prolog. Two ways have been explored to resolve these problems: loop checking and tabling. Loop checking can cut infinite loops, but it cannot be both sound and complete even for functionfree logic programs. Tabling seems ..."
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Cited by 15 (8 self)
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Infinite loops and redundant computations are long recognized open problems in Prolog. Two ways have been explored to resolve these problems: loop checking and tabling. Loop checking can cut infinite loops, but it cannot be both sound and complete even for functionfree logic programs. Tabling seems to be an effective way to resolve infinite loops and redundant computations. However, existing tabulated resolutions, such as OLDTresolution, SLGresolution, and Tabulated SLSresolution, are nonlinear because they rely on the solutionlookup mode in formulating tabling. The principal disadvantage of nonlinear resolutions is that they cannot be implemented using a simple stackbased memory structure like that in Prolog. Moreover, some strictly sequential operators such as cuts may not be handled as easily as in Prolog. In this paper, we propose a hybrid method to resolve infinite loops and redundant computations. We combine the ideas of loop checking and tabling to establish a linear tabulated resolution called TPresolution. TPresolution has two distinctive features: (1) It makes linear tabulated derivations in the same way as Prolog except that infinite loops are broken and redundant computations are reduced. It handles cuts as effectively as Prolog. (2) It is sound and complete for positive logic programs with the boundedtermsize property. The underlying algorithm can be implemented by an extension to any existing Prolog abstract machines such as WAM or ATOAM.
Consequencefinding based on ordered linear resolution
 In proc of IJCAI
, 1991
"... Since linear resolution with clause ordering is incomplete for consequencefinding, it has been used mainly for prooffinding. In this paper, we reevaluate consequencefinding. Firstly, consequencefinding is generalized to the problem in which only interesting clauses having a certain property (ca ..."
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Cited by 15 (0 self)
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Since linear resolution with clause ordering is incomplete for consequencefinding, it has been used mainly for prooffinding. In this paper, we reevaluate consequencefinding. Firstly, consequencefinding is generalized to the problem in which only interesting clauses having a certain property (called characteristic clauses) should be found. Then, we show how adding a skip rule to ordered linear resolution makes it complete for consequencefinding in this general sense. Compared with setofsupport resolution, the proposed method generates fewer clauses to find such a subset of consequences. In the propositional case, this is an elegant tool for computing the prime implicants/implicates. The importance of the results lies in their applicability to a wide class of AI problems including procedures for nonmonotonic and abductive reasoning and truth maintenance systems. 1
Computational Logic and Human Thinking: How to be Artificially Intelligent
, 2011
"... The mere possibility of Artificial Intelligence (AI) – of machines that can think and act as intelligently as humans – can generate strong emotions. While some enthusiasts are excited by the thought that one day machines may become more intelligent than people, many of its critics view such a prosp ..."
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Cited by 13 (7 self)
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The mere possibility of Artificial Intelligence (AI) – of machines that can think and act as intelligently as humans – can generate strong emotions. While some enthusiasts are excited by the thought that one day machines may become more intelligent than people, many of its critics view such a prospect with horror. Partly because these controversies attract so much attention, one of the most important accomplishments of AI has gone largely unnoticed: the fact that many of its advances can also be used directly by people, to improve their own human intelligence. Chief among these advances is Computational Logic. Computational Logic builds upon traditional logic, which was originally developed to help people think more effectively. It employs the techniques of symbolic logic, which has been used to build the foundations of mathematics and computing. However, compared with traditional logic, Computational Logic is much more powerful; and compared with symbolic logic, it is much simpler and more practical. Although the applications of Computational Logic in AI require the use of mathematical notation, its human applications do not. As a consequence, I have written the main part of this book informally, to reach as wide an audience as possible. Because human thinking is also the subject of study in many other fields, I have drawn upon related studies in Cognitive Psychology, Linguistics, Philosophy, Law, Management Science and English
The Inverse Method
, 2001
"... this paper every formula is equivalent to a formula in negation normal form ..."
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Cited by 12 (1 self)
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this paper every formula is equivalent to a formula in negation normal form
Autarky pruning in propositional model elimination reduces failure redundancy
 Journal of Automated Reasoning
, 1999
"... Goalsensitive resolution methods, such as Model Elimination, have been observed to have a higher degree of search redundancy than modelsearch methods, Therefore, resolution methods have not been seen in high performance propositional satis ability testers. A method to reduce search redundancy in g ..."
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Cited by 12 (3 self)
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Goalsensitive resolution methods, such as Model Elimination, have been observed to have a higher degree of search redundancy than modelsearch methods, Therefore, resolution methods have not been seen in high performance propositional satis ability testers. A method to reduce search redundancy in goalsensitive resolution methods is introduced. The idea at the heart of the method is to attempt to construct a refutation and a model simultaneously and incrementally, based on subsearch outcomes. The method exploits the concept of \autarky&quot;, which can be informally described as a \selfsu cient &quot; model for some clauses, but which does not a ect the remaining clauses of the formula. Incorporating this method into Model Elimination leads to an algorithm called Modoc. Modoc is shown, both analytically and experimentally, to be faster than Model Elimination by an exponential factor. Modoc, unlike Model Elimination, is able to nd a model if it fails to nd a refutation, essentially by combining autarkies. Unlike the pruning strategies of most re nements of resolution, autarkyrelated pruning does not prune any successful refutation; it only prunes attempts that ultimately will be unsuccessful; consequently, it will not force the underlying Modoc search to nd an unnecessarily long refutation. To prove correctness and other properties, a game characterization of refutation search isintroduced, which demonstrates
A Propositional Theorem Prover to Solve Planning and Other Problems
 Annals of Mathematics and Artificial Intelligence
, 1998
"... Classical STRIPSstyle planning problems are formulated as theorems to be proven from a new point of view. The result for a refutationbased theorem prover may be a propositional formula that is to be proven unsatisfiable. This formula is identical to the formula that may be derived directly by vari ..."
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Cited by 10 (4 self)
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Classical STRIPSstyle planning problems are formulated as theorems to be proven from a new point of view. The result for a refutationbased theorem prover may be a propositional formula that is to be proven unsatisfiable. This formula is identical to the formula that may be derived directly by various "sat compilers", but the theoremproving view provides valuable additional information not in the formula: namely, the theorem to be proven. Traditional satisfiability methods, most of which are based on model search, are unable to exploit this additional information. However, a new algorithm, called "Modoc", is able to exploit this information and has achieved performance comparable or superior to the fastest known satisfiability methods, including stochastic search methods, on planning problems that have been reported by other researchers, as well as formulas derived from other applications. Unlike most theorem provers, Modoc performs well on both satisfiable and unsatisfiable formulas...