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522
Semantic Issues in Deductive Databases and Logic Programs
 Formal Techniques in Artificial Intelligence
, 1990
"... this paper. In particular, the paper reports on a very significant progress made recently in this area. It also presents some results which have not yet appeared in print. The paper is organized as follows. In the next two sections we define deductive databases and logic programs. Subsequently, in ..."
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Cited by 54 (12 self)
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this paper. In particular, the paper reports on a very significant progress made recently in this area. It also presents some results which have not yet appeared in print. The paper is organized as follows. In the next two sections we define deductive databases and logic programs. Subsequently, in Sections 4 and 5, we discuss model theory and fixed points, which play a crucial role in the definition of semantics. Section 6 is the main section of the paper and is entirely devoted to a systematic exposition and comparison of various proposed semantics. In Section 7 we discuss the relationship between declarative semantics of deductive databases and logic programs and nonmonotonic reasoning. Section 8 contains concluding remarks. 2 Deductive Databases
Manyvalued logic
 Handbook of Philosophical Logic
, 1986
"... ABSTRACT. This paper discusses the general problem of translation functions between logics, given in axiomatic form, and in particular, the problem of determining when two such logics are “synonymous ” or “translationally equivalent. ” We discuss a proposed formal definition of translational equival ..."
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Cited by 54 (1 self)
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ABSTRACT. This paper discusses the general problem of translation functions between logics, given in axiomatic form, and in particular, the problem of determining when two such logics are “synonymous ” or “translationally equivalent. ” We discuss a proposed formal definition of translational equivalence, show why it is reasonable, and also discuss its relation to earlier definitions in the literature. We also give a simple criterion for showing that two modal logics are not translationally equivalent, and apply this to wellknown examples. Some philosophical morals are drawn concerning the possibility of having two logical systems that are “empirically distinct ” but are both translationally equivalent to a common logic. KEY WORDS: modal logic, synonymy, translation 1.
Logic program specialisation through partial deduction: Control issues
 THEORY AND PRACTICE OF LOGIC PROGRAMMING
, 2002
"... Program specialisation aims at improving the overall performance of programs by performing source to source transformations. A common approach within functional and logic programming, known respectively as partial evaluation and partial deduction, is to exploit partial knowledge about the input. It ..."
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Cited by 54 (12 self)
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Program specialisation aims at improving the overall performance of programs by performing source to source transformations. A common approach within functional and logic programming, known respectively as partial evaluation and partial deduction, is to exploit partial knowledge about the input. It is achieved through a wellautomated application of parts of the BurstallDarlington unfold/fold transformation framework. The main challenge in developing systems is to design automatic control that ensures correctness, efficiency, and termination. This survey and tutorial presents the main developments in controlling partial deduction over the past 10 years and analyses their respective merits and shortcomings. It ends with an assessment of current achievements and sketches some remaining research challenges.
Some lambda calculus and type theory formalized
 Journal of Automated Reasoning
, 1999
"... Abstract. We survey a substantial body of knowledge about lambda calculus and Pure Type Systems, formally developed in a constructive type theory using the LEGO proof system. On lambda calculus, we work up to an abstract, simplified, proof of standardization for beta reduction, that does not mention ..."
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Cited by 53 (7 self)
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Abstract. We survey a substantial body of knowledge about lambda calculus and Pure Type Systems, formally developed in a constructive type theory using the LEGO proof system. On lambda calculus, we work up to an abstract, simplified, proof of standardization for beta reduction, that does not mention redex positions or residuals. Then we outline the meta theory of Pure Type Systems, leading to the strengthening lemma. One novelty is our use of named variables for the formalization. Along the way we point out what we feel has been learned about general issues of formalizing mathematics, emphasizing the search for formal definitions that are convenient for formal proof and convincingly represent the intended informal concepts.
Structural Cut Elimination  I. Intuitionistic and Classical Logic
 Information and Computation
, 2000
"... this paper we present new proofs of cut elimination for intuitionistic and classical sequent calculi and give their representations in the logical framework LF [HHP93] as implemented in the Elf system [Pfe91]. Multisets are avoided altogether in these proofs, and termination measures are replaced b ..."
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Cited by 53 (17 self)
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this paper we present new proofs of cut elimination for intuitionistic and classical sequent calculi and give their representations in the logical framework LF [HHP93] as implemented in the Elf system [Pfe91]. Multisets are avoided altogether in these proofs, and termination measures are replaced by three nested structural inductions. Parameters are treated as variables bound in derivations, thus naturally capturing occurrence conditions. A starting point for the proofs is Kleene's sequent system G 3 [Kle52], which we derive systematically from the point of view that a sequent calculus should be a calculus of proof search for natural deductions. It can easily be related to Gentzen's original and other sequent calculi. We augment G 3 with proof terms that are stable under weakening. These proof terms enable the structural induction and furthermore form the basis of the representation of the proof in LF. The most closely related work on cut elimination is MartinLo# f 's proof of admissibility [ML68]. In MartinLo# f 's system the cut rule incorporates aspects of both weakening and contraction which enables a structural induction argument closely related to ours. However, without the introduction of proof terms, the implicit weakening in the cut rule makes it difficult to implement this proof directly. Herbelin [Her95] restates this proof and proceeds by assigning proof terms only to restricted sequent calculi LJT and LKT which correspond more immediately to
Algebras of feasible functions
 in "Proc. 24th Annual IEEE Sympos. Found. Comput. Sci
, 1983
"... What happens if we interpret the syntax of primitive recursive functions in finite domains rather than in the (Platonic) realm of all natural numbers? The answer is somewhat surprising: primitive recursiveness coincides with LOGSPACE computability. Analogously, recursiveness coincides with PTIME com ..."
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Cited by 50 (5 self)
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What happens if we interpret the syntax of primitive recursive functions in finite domains rather than in the (Platonic) realm of all natural numbers? The answer is somewhat surprising: primitive recursiveness coincides with LOGSPACE computability. Analogously, recursiveness coincides with PTIME computability on finite domains (cf. [Sa]). Inductive definitions for some other complexity classes are discussed too.
MultiValued Symbolic ModelChecking
 ACM TRANSACTIONS ON SOFTWARE ENGINEERING AND METHODOLOGY
, 2003
"... This paper introduces the concept and the general theory of multivalued model checking, and describes a multivalued symbolic modelchecker \Chi Chek. Multivalued ..."
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Cited by 50 (16 self)
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This paper introduces the concept and the general theory of multivalued model checking, and describes a multivalued symbolic modelchecker \Chi Chek. Multivalued
Reasoning Theories  Towards an Architecture for Open Mechanized Reasoning Systems
, 1994
"... : Our ultimate goal is to provide a framework and a methodology which will allow users, and not only system developers, to construct complex reasoning systems by composing existing modules, or to add new modules to existing systems, in a "plug and play" manner. These modules and systems might be ..."
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Cited by 47 (11 self)
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: Our ultimate goal is to provide a framework and a methodology which will allow users, and not only system developers, to construct complex reasoning systems by composing existing modules, or to add new modules to existing systems, in a "plug and play" manner. These modules and systems might be based on different logics; have different domain models; use different vocabularies and data structures; use different reasoning strategies; and have different interaction capabilities. This paper makes two main contributions towards our goal. First, it proposes a general architecture for a class of reasoning systems called Open Mechanized Reasoning Systems (OMRSs). An OMRS has three components: a reasoning theory component which is the counterpart of the logical notion of formal system, a control component which consists of a set of inference strategies, and an interaction component which provides an OMRS with the capability of interacting with other systems, including OMRSs and hum...
A proof of the turingcompleteness of xslt and xquery
 In Technical report SFB 441, Eberhard Karls Universitat Tubingen
, 2004
"... The World Wide Web Consortium recommends both XSLT and XQuery as query languages for XML documents. XSLT, originally designed to transform XML into HTML, is nowadays a fully grown XML query language that is mostly suited for use by machines. XQuery on the other hand was particularly designed to be e ..."
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Cited by 47 (0 self)
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The World Wide Web Consortium recommends both XSLT and XQuery as query languages for XML documents. XSLT, originally designed to transform XML into HTML, is nowadays a fully grown XML query language that is mostly suited for use by machines. XQuery on the other hand was particularly designed to be easily used by humans. Since both query languages receive a steady growth in user acceptance, it is important and natural to ask about their expressive power. We show here that both XSLT and XQuery are Turingcomplete by reduction to µrecursive functions. Keywords: XML, XSLT, XQuery, Turingcompleteness 1