In this paper we investigate the fragment of intuitionistic logic which only uses conjunction (meet) and implication, using finite duality for distributive lattices and universal models. We give a description of the finitely generated universal models of this fragment and give a complete characterization of the up-sets of Kripke models of intuitionistic logic which can be defined by meet-implic...

Modern binary informatics with its so-called ―classical‖ two-valued logic admits to create an artificial intellect and suppresses the natural intellect of students and other thinking people. Logic that based on dogmatic law of the excluded middle is incompatible with dialectical principle of opposition coexistence. Such logic is deprived of fundamental logical relation – the content consequence...

This paper deals with learning implication relations from some kinds of knowledge (statistical studies, possibilistic information or possible worlds) about truth valuations on a set of propositions. An induction principle is considered in each one of this cases. If only the possible valuations are known, then it is checked when two families of possible valuations produce the same implication. A...

A quasi-implication algebra is introduced as an algebraic counterpart of an implication reduct of propositional logic having noninvolutory negation (e.g. intuitionistic logic). We show that every pseudocomplemented semilattice induces a quasi-implication algebra (but not conversely). On the other hand, a more general algebra, a so-called pseudocomplemented q-semilattice is introduced and a mutu...

Both propositional dependence logic and inquisitive logic are expressively complete. As a consequence, every formula in the language of inquisitive logic with intuitionistic disjunction or intuitionistic implication can be translated equivalently into a formula in the language of propositional dependence logic without these two connectives. We show that although such a (noncompositional) transl...

the aim of this paper is to introduce the notions of ($epsilon, epsilon vee q$)-fuzzy p-ideals, ($epsilon, epsilon vee q$)-fuzzy q-ideals and ($epsilon, epsilon vee q$)-fuzzy a-ideals in bcialgebras and to investigate some of their properties. several characterizationtheorems for these generalized fuzzy ideals are proved and the relationshipamong these generalized fuzzy ideals of bci-algebras i...

Professor Rasiowa [HR49] considers implication algebras (A,⇒, V ) such that ⇒ is a binary operation on the universe A and V ∈ A. In particular, there are studied implicative algebras, positive implication algebras and implication algebras; the second kind corresponds to the logic of positive implication, and the third one to the logic of classical implication. In each case, the distinguished el...

The new …eld of judgment aggregation aims to …nd group judgments on logically interconnected propositions. Recent impossibility results have established limitations on the possibility to vote independently on the propositions, hence notably on the possibility to use quota rules (rules with acceptance thresholds for the propositions). I show that, fortunately, the impossibilities fail to apply t...

Conditionals play crucial roles in human reasoning. They represent rules, causal relationship, and explicit inference. Psychology of reasoning, from its inception, has been studying how humans use and understand conditionals. One prominent feature of humans’ conditionals is that it does not follow the pattern of the standard model of conditionals. In classical logic, the corresponding connectiv...