Constructive Discursive Logic: Paraconsistency in Constructivism
نویسندگان
چکیده
We propose a constructive discursive logic with strong negation CDLSN based on Nelson’s constructive logic N as a constructive version of Jaśkowski’s discursive logic. In CDLSN, discursive negation is defined similar to intuitionistic negation and discursive implication is defined as material implication using discursive negation. We give an axiomatic system and Kripke semantics with a completeness proof. We also discuss some possible applications of CDLSN for common-sense reasoning.
منابع مشابه
Suprema in Ordered Vector Spaces: a Constructive Approach
Ordered vector spaces are examined from the point of view of Bishop’s constructive mathematics, which can be viewed as the constructive core of mathematics. Two different (but classically equivalent) notions of supremum are investigated in order to illustrate some features of constructive mathematics. By using appropriate definitions of the partial order set, supremum, and ordered vector space,...
متن کاملImplicit Epistemic Aspects of Constructive Logic
In the present paper I wish to regard constructive logic as a self-contained system for the treatment of epistemological issues; the explanations of the constructivist logical notions are cast in an epistemological mold already from the outset. The discussion offered here intends to make explicit this implicit epistemic character of constructivism. Particular attention will be given to the inte...
متن کاملA Constructive Epistemic Logic with Public Announcement (Non-Predetermined Possibilities)
We argue that the notion of epistemic possible worlds in constructivism (intuition-ism) is not as the same as it is in classic view, and there are possibilities, called non-predetermined worlds, which are ignored in (classic) Epistemic Logic. Regarding non-predetermined possibilities, we propose a constructive epistemic logic and prove soundness and completeness theorems for it. We extend the p...
متن کاملThe Social and Discursive Construction of New Information Technologies
Social constructivism provides a fruitful approach for understanding new information technologies. Some leading ideas of social constructivism are introduced, and a discursive reading is given of a model that integrates them: Collins’s “empirical programme of relativism” (EPOR). The importance of discourse in the social construction of technologies is illustrated by the construction of meanings...
متن کاملOn the "Logic without Borders" Point of View
Finitism, intuitionism, constructivism, formalism, predicativism, structuralism, objectivism, platonism; foundationalism, anti-foundationalism, first orderism; constructive type theory, Cantorian set theory, proof theory; top down principles or building up from below—framework commitments, that is, ideology, permeates the logician’s mathematical life. Such commitments set ∗This paper is based o...
متن کامل