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and Deduction Systems
"... Manipulation of Boolean functions has important applications in such fields as hardware verification, nonmonotonic reasoning, and decision support. Most often, in such applications, the set of prime implicates/implicants of a large formula must be computed. Many algorithms have been proposed to com ..."
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Manipulation of Boolean functions has important applications in such fields as hardware verification, nonmonotonic reasoning, and decision support. Most often, in such applications, the set of prime implicates/implicants of a large formula must be computed. Many algorithms have been proposed to compute the prime implicates of propositionalBoolean formulas, e.g. [4, 5]. Most of them assume that the input is in conjunctive/disjunctive normal form (CNF/DNF). The bottleneck of such algorithms is usually the large number of subsumed (i.e. nonminimal) disjunctive/conjunctive paths through the given formula. Therefore, it is crucial to remove as much redundancy of this kind as possible, before any explicit enumeration of prime implicates/implicants starts. Even if such explicit computation of prime implicates/implicants is not an immediate goal, removing any redundancies due to subsumed disjunctive/conjunctive paths is usually highly desirable. Among the most successful methods used to deal with this task are binary decision diagrams (BDDs) [2, 3]. It is, however, well known that BDD methods do not work well on some classes of formulas, in particular, when they are used to compute prime implicants. Another restriction of BDDs is that they (at least the efficient versions) essentially produce an XORAND normal form, but this is not always what is needed.
System Description: Twelf  A MetaLogical Framework for Deductive Systems
 Proceedings of the 16th International Conference on Automated Deduction (CADE16
, 1999
"... . Twelf is a metalogical framework for the specification, implementation, and metatheory of deductive systems from the theory of programming languages and logics. It relies on the LF type theory and the judgmentsastypes methodology for specification [HHP93], a constraint logic programming interp ..."
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Cited by 355 (54 self)
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. Twelf is a metalogical framework for the specification, implementation, and metatheory of deductive systems from the theory of programming languages and logics. It relies on the LF type theory and the judgmentsastypes methodology for specification [HHP93], a constraint logic programming
Minimal Deductive Systems for RDF
 In ESWC
, 2007
"... Abstract This paper presents a minimalist program for RDF, by showing how one can do without several predicates and keywords of the RDF Schema vocabulary, obtaining a simpler language which preserves the original semantics. This approach is beneficial in at least two directions: (a) To have a simple ..."
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Cited by 71 (9 self)
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that it encompasses the main features of RDFS; a formal semantics and a deductive system for it; sound and complete deductive systems for their subfragments; and an O(n log n) complexity bound for ground entailment in this fragment. 1
Labelled deductive system for semantic . . .
"... In this paper we describe correct and complete Kripkestyle semantics for the labelled deductive system which is proposed for ..."
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In this paper we describe correct and complete Kripkestyle semantics for the labelled deductive system which is proposed for
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 21 (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
The PADDY Partial Deduction System
, 1992
"... This report describes the PADDY partial deduction system. Its main features are that it can handle full Sepia, including advanced features; is automatic; always terminates; is provably correct on pure Prolog programs; uses a powerful adaptive transformation strategy; has fast transformation times; i ..."
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Cited by 16 (0 self)
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This report describes the PADDY partial deduction system. Its main features are that it can handle full Sepia, including advanced features; is automatic; always terminates; is provably correct on pure Prolog programs; uses a powerful adaptive transformation strategy; has fast transformation times
Automating the Meta Theory of Deductive Systems
, 2000
"... This thesis describes the design of a metalogical framework that supports the representation and verification of deductive systems, its implementation as an automated theorem prover, and experimental results related to the areas of programming languages, type theory, and logics. Design: The meta ..."
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Cited by 87 (16 self)
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This thesis describes the design of a metalogical framework that supports the representation and verification of deductive systems, its implementation as an automated theorem prover, and experimental results related to the areas of programming languages, type theory, and logics. Design: The meta
Fibring Labelled Deduction Systems
 Journal of Logic and Computation
, 2002
"... We give a categorial characterization of how labelled deduction systems for logics with a propositional basis behave under unconstrained fibring and under fibring that is constrained by symbol sharing. At the semantic level, we introduce a general semantics for our systems and then give a categorial ..."
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Cited by 16 (9 self)
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We give a categorial characterization of how labelled deduction systems for logics with a propositional basis behave under unconstrained fibring and under fibring that is constrained by symbol sharing. At the semantic level, we introduce a general semantics for our systems and then give a
The CORAL Deductive System
 THE VLDB JOURNAL
, 1994
"... CORAL is a deductive system which supports a rich declarative language, and an interface to C++ which allows for a combination of declarative and imperative programming. The declarative query language supports general Horn clauses augmented with complex terms, setgrouping, aggregation, negation, ..."
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Cited by 28 (2 self)
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CORAL is a deductive system which supports a rich declarative language, and an interface to C++ which allows for a combination of declarative and imperative programming. The declarative query language supports general Horn clauses augmented with complex terms, setgrouping, aggregation, negation
Grammars, Deductive Systems, and Parsing
 Invited talk at the ESF Conference on Logic, Language and Information, Autrans
, 1992
"... Many theories of grammar and styles of grammar specification have stemmed from mathematical logic, computer science, and computational linguistics, and have been used for describing natural languages. By a series of constructions, we relate categorial, attribute and logic grammars via (axiomatic) la ..."
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Cited by 1 (1 self)
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) labelled deductive systems, and extend this relation to accommodate unificationbased grammars and socalled Montague Grammar. The axioms of a labelled deductive system can also be used to constrain the proof search by automatically generating an LR parser from them; we describe the implementation
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