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The Role of Deduction Rules in Semantics
 Journal of Semantics
, 1988
"... The distinction between 'partial ' and 'total ' interpretations (models) is discussed and related to the distinction between prooftheoretical and modeltheoretical treatments of logic. It is claimed that there is a parallel between the construction of a proof based on a set of p ..."
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of premises and e.g. the production of a naturallanguage text which is based on information in some kind of database. The main part of the paper is devoted to a discussion of the relations between the deduction rules traditionally associated with the existential quantifier and notions pertaining
Quantum deduction rules
, 2007
"... We define propositional quantum Frege proof systems and compare it with classical Frege proof systems. ..."
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We define propositional quantum Frege proof systems and compare it with classical Frege proof systems.
Quantum deduction rules
, 2007
"... Abstract We define propositional quantum Frege proof systems and compare it with classical Frege proof systems. ..."
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Abstract We define propositional quantum Frege proof systems and compare it with classical Frege proof systems.
Natural deduction: ∀rules
, 2011
"... Goal: an uncommon but useful approach to logic: minimal logic + ∃̃, ∨ ̃ (weak, classical) and ∃, ∨ (strong, constructive). 1. Embedding classical and intuitionistic logic into minimal logic. 2. Geometric formulas G and geometric implications Γ. Γ `c G implies Γ `i G. 3. Extended geometric implicatio ..."
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Goal: an uncommon but useful approach to logic: minimal logic + ∃̃, ∨ ̃ (weak, classical) and ∃, ∨ (strong, constructive). 1. Embedding classical and intuitionistic logic into minimal logic. 2. Geometric formulas G and geometric implications Γ. Γ `c G implies Γ `i G. 3. Extended geometric implications: → occurs positively only. 4. ∃̃, ∨ ̃ versus ∃,∨: variants of Barr’s theorem. 5. Examples.
Number of symbols in Frege proofs with and without the deduction rule
, 2004
"... Frege systems with the deduction rule produce at most quadratic speedup over Frege systems using as a measure of length the number of symbols in the proof. We study whether that speedup is in reality smaller. We show that the speedup is linear when the Frege proofs are treelike. Also, two groups o ..."
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Frege systems with the deduction rule produce at most quadratic speedup over Frege systems using as a measure of length the number of symbols in the proof. We study whether that speedup is in reality smaller. We show that the speedup is linear when the Frege proofs are treelike. Also, two groups
Deductive rules in holographic reduced representation
, 2005
"... Communicated by T. Heskes Holographic reduced representation is based on a suitable distributive coding of structured information in conceptual vectors, which elements satisfy normal distribution N(0,1/n). Existing applications of this approach concern various models of associative memory that explo ..."
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that exploit a simple algebraic operation of scalar product of distributed representations to measure an overlap between two structured concepts. This paper describes an inference process based on the rules modus ponens and modus tollens. r 2006 Elsevier B.V. All rights reserved.
On the Deduction Rule and the Number of Proof Lines (Extended Abstract)
"... We introduce new proof systems for propositional logic, simple deduction Frege systems, general deduction Frege systems and nested deduction Frege systems, which augment Frege systems with variants of the deduction rule. We give upper bounds on the lengths of proofs in these systems compared to l ..."
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We introduce new proof systems for propositional logic, simple deduction Frege systems, general deduction Frege systems and nested deduction Frege systems, which augment Frege systems with variants of the deduction rule. We give upper bounds on the lengths of proofs in these systems compared
An Open Architecture for Optimizing Active and Deductive Rules
, 1993
"... It is evident that nontraditional applications, such as engineering design, Air Traffic Control, situation assessment, Computer integrated manufacturing, program trading and cooperative problem solving require both deductive and active capabilities in addition to the functionality provided by a ..."
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traditional DBMS. In this paper, we propose an extensible query optimizer architecture for supporting both active and deductive rules. We first discuss the similarities and differences of the optimization techniques used in deductive and active databases, analyze them and then propose an extensible
The Deduction Rule and Linear and Nearlinear Proof Simulations
"... ... that a Frege proof of n lines can be transformed into a treelike Frege proof of O(n log n) lines and of height O(log n). As a corollary of this fact we can prove that natural deduction and sequent calculus treelike systems simulate Frege systems with proof lengths bounded by O(n log n). ..."
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... that a Frege proof of n lines can be transformed into a treelike Frege proof of O(n log n) lines and of height O(log n). As a corollary of this fact we can prove that natural deduction and sequent calculus treelike systems simulate Frege systems with proof lengths bounded by O(n log n).
THE DATALOG DL COMBINATION OF DEDUCTION RULES AND DESCRIPTION LOGICS
"... Uniting ontologies and rules has become a central topic in the Semantic Web. Bridging the discrepancy between these two knowledge representations, this paper introduces Datalog DL as a family of hybrid languages, where Datalog rules are parameterized by various DL (description logic) languages rang ..."
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Uniting ontologies and rules has become a central topic in the Semantic Web. Bridging the discrepancy between these two knowledge representations, this paper introduces Datalog DL as a family of hybrid languages, where Datalog rules are parameterized by various DL (description logic) languages
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