Since Brouwer has proclaimed in 1908 the untrustworthiness of classical logic by rejecting the law of the excluded middle, intuitionistic logic, managing without this law, began little by little to develop. As a calculus, it has been presented in a wellknown paper of Heyting (1930), preceded by the interesting papers of A. N. Kolmogorov (1925) and V. I. Glivenko (1929). Soon after that, Kolmogo...

We introduce distributive unimodal logic as a modal logic of binary relations over posets which naturally generalizes the classical modal logic of binary relations over sets. The relational semantics of this logic is similar to the relational semantics of intuitionistic modal logic and positive modal logic, but it generalizes both of these by placing no restrictions on the accessibility relatio...

In this paper one generalizes the intuitionistic fuzzy logic (IFL) and other logics to neutrosophic logic (NL). The differences between IFL and NL (and the corresponding intuitionistic fuzzy set and neutrosophic set) are pointed out.

Abstract In the style of Lindström’s theorem for classical first-order logic, this article characterizes propositional bi-intuitionistic logic as maximal (with respect to expressive power) abstract satisfying a certain form compactness, Tarski union property and preservation under bi-asimulations. Since introduces new complexities in intuitionistic setting by adding analogue backwards looking m...

We describe a method for obtaining classical logic from intuitionistic logic which does not depend on any proof system, and show that by applying it to the most important implicational relevance logics we get relevance logics with nice semantical and proof-theoretical properties. Semantically all these logics are sound and strongly complete relative to classes of structures in which all element...

In this paper, we present the interval neutrosophic logics which generalizes the fuzzy logic, paraconsistent logic, intuitionistic fuzzy logic and many other non-classical and non-standard logics. We will give the formal definition of interval neutrosophic propositional calculus and interval neutrosophic predicate calculus. Then we give one application of interval neutrosophic logics to do appr...

Hyland, M. and V. de Paiva, Full intuitionistic linear logic (extended abstract), Annals of Pure and Applied Logic 64 (1993) 273-291. In this paper we give a brief treatment of a theory of proofs for a system of Full Intuitionistic Linear Logic. This system is distinct from Classical Linear Logic, but unlike the standard Intuitionistic Linear Logic of Girard and Lafont includes the multiplicati...

It has been shown that from the purely mathematical viewpoint, the (traditional) intuitionistic fuzzy logic is equivalent to interval-valued fuzzy logic. In this paper, we show that if we go beyond the traditional “and”and “or”-operations, then intuitionistic fuzzy logic becomes more general than the interval-valued one.

We propose a new bi-intuitionistic type theory called Dualized Type Theory (DTT). It is a type theory with perfect intuitionistic duality, and corresponds to a single-sided polarized sequent calculus. We prove DTT strongly normalizing, and prove type preservation. DTT is based on a new propositional bi-intuitionistic logic called Dualized Intuitionistic Logic (DIL) that builds on Pinto and Uust...