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The Longest Perpetual Reductions in Orthogonal Expression Reduction Systems
 In: Proc. of the 3 rd International Conference on Logical Foundations of Computer Science, LFCS'94, A. Nerode and Yu.V. Matiyasevich, eds., Springer LNCS
, 1994
"... We consider reductions in Orthogonal Expression Reduction Systems (OERS), that is, Orthogonal Term Rewriting Systems with bound variables and substitutions, as in the calculus. We design a strategy that for any given term t constructs a longest reduction starting from t if t is strongly normaliza ..."
Abstract

Cited by 18 (8 self)
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We consider reductions in Orthogonal Expression Reduction Systems (OERS), that is, Orthogonal Term Rewriting Systems with bound variables and substitutions, as in the calculus. We design a strategy that for any given term t constructs a longest reduction starting from t if t is strongly normalizable, and constructs an infinite reduction otherwise. The Conservation Theorem for OERSs follows easily from the properties of the strategy. We develop a method for computing the length of a longest reduction starting from a strongly normalizable term. We study properties of pure substitutions and several kinds of similarity of redexes. We apply these results to construct an algorithm for computing lengths of longest reductions in strongly persistent OERSs that does not require actual transformation of the input term. As a corollary, we have an algorithm for computing lengths of longest developments in OERSs. 1 Introduction A strategy is perpetual if, given a term t, it constructs an infinit...
Realizability algebras II: new models of ZF + DC
, 2010
"... The technology of classical realizability was developed in [15, 18] in order to extend the proofprogram correspondence (also known as CurryHoward correspondence) from pure intuitionistic logic to the whole of mathematical proofs, with excluded middle, axioms of ZF, dependent choice, existence of a ..."
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The technology of classical realizability was developed in [15, 18] in order to extend the proofprogram correspondence (also known as CurryHoward correspondence) from pure intuitionistic logic to the whole of mathematical proofs, with excluded middle, axioms of ZF, dependent choice, existence of a well ordering on P (N),...
unknown title
"... The formal expression of pro positional attitudes, especially when nested (iterated), is an important problem for AI. An interesting firstorder extensional logical system for such expression has been proposed by Creary. In this system concepts (and concepts of concepts, etc.) are made explicit. The ..."
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The formal expression of pro positional attitudes, especially when nested (iterated), is an important problem for AI. An interesting firstorder extensional logical system for such expression has been proposed by Creary. In this system concepts (and concepts of concepts, etc.) are made explicit. The system includes &quot;concept functions&quot;, which are special functions which act on and deliver concepts. We point out a difficulty with these functions. A alternative system is proposed, in which there is a conceptforming function corresponding roughly to complexconcept formers (especially the phrase &quot;the proposition that&quot;) implicit in English sentences. The resulting system has a more primitive and natural notional base than Creary's has. We avoid problems with quantification inside propositions which are the objects of propositional attitudes by recasting quantified expressions into variablefree form by means of certain functions (&quot;combinators&quot;). I