The paper presents a constructive interpretation for proofs in classical logic of 0 1 sentences and for a witness extraction procedure based on Prawitz's reduction rules.

Intuitionistic Type Theory (also Constructive Type Theory or Martin-Löf Type Theory) is a formal logical system and philosophical foundation for constructive mathematics (link). It is a fullscale system which aims to play a similar role for constructive mathematics as Zermelo-Fraenkel Set Theory (link) does for classical mathematics. It is based on the propositions-as-types principle and clarif...

The purpose of this study was to analyze the relationship between the sunk cost effect and ambiguity in investment situations. Starting from the sensemaking approach and the decision dilemma theory, our hypothesis is that a sunk cost affected decision can be “constructively" rational in ambiguous environments in the sense that decision makers have the opportunity, through actions, to enact an e...

This paper applies a new methodology for analyzing and interpreting IP metrics collected by active measurement to loss traces aggregated on the Internet. This new approach is based on inferring traffic characteristics that lead to the observed loss trace based on an associated a priori constructive model. The constructive model used in this paper is an MMPP/M/1/N single server bottleneck. The o...

Dynamical algebraic structures, pointfree topological spaces and Hilbert’s program A possible relevant meaning of Hilbert’s program is the following one : “give a constructive semantic for classical mathematics”. More precisely, give a systematic interpretation of classical abstract proofs (that use Third Excluded Middle and Choice) about abstract objects, as constructive proofs about construct...

We introduce an abstract algebraic structure — a lattice defined on a generalized truth value space of constructive logic. For background one can refer to the idea of ‘under-determined’ and ‘over-determined’ valuations (Dunn), a ‘useful four-valued logic’ (Belnap), and the notion of a bilattice (Ginsberg). We consider within one general framework the notions of constructive truth and constructi...

This paper is seeking to deal with studying the methods of employing traditions in ‘Al-Furghan Fi Tafsir Al-Quran Bel-Quran’ written by Ayatollah Muhammad Sadeghi Tehrani in a methodological approach. His method of interpretation is the Quran by the Quran. This method has been observed all over of this work. However, this method does not prevent employing traditions for understandin...

In constructive algebra one cannot in general decide the irreducibility of a polynomial over a field K. This poses some problems to showing the existence of the algebraic closure of K. We give a possible constructive interpretation of the existence of the algebraic closure of a field in characteristic 0 by building, in a constructive metatheory, a suitable site model where there is such an alge...