One of the key features of logic programming is the notion of goal-directed prov-ability. In intuitionistic logic, the notion of uniform proof has been used as a proof-theoretic characterization of this property. Whilst the connections between intuition-istic logic and computation are well known, there is no reason per se why a similar notion cannot be given in classical logic. In this paper we...

We show that simultaneous rigid E-unification, or SREU for short, is decidable and in fact EXPTIME-complete in the case of one variable. This result implies that the ∀∗∃∀∗ fragment of intuitionistic logic with equality is decidable. Together with a previous result regarding the undecidability of the ∃∃-fragment, we obtain a complete classification of decidability of the prenex fragment of intui...

We give a semantic proof that every term of a combi-nator version of system F has a normal form. As the argument is entirely formalisable in an impredicative constructive type theory a reduction-free normalisation algorithm can be extracted from this. The proof is presented as the construction of a model of the calculus inside a category of presheaves. Its deenition is given entirely in terms o...

An intuitionistic, hybrid modal logic suitable for reasoning about distribution of resources was introduced in [14, 15]. The modalities of the logic allow us to validate properties in a particular place, in some place and in all places. We give a sound and complete Kripke semantics for the logic extended with disjunctive connectives. The extended logic can be seen as an instance of Hybrid IS5. ...

The interval-valued intuitionistic fuzzy set (IVIFS) which is an extension of the Atanassov’s intuitionistic fuzzy set is a powerful tool for modeling real life decision making problems. In this paper, we propose the emph{generalized interval-valued intuitionistic fuzzy Hamacher generalized Shapley Choquet integral} (GIVIFHGSCI) and the emph{interval-valued intuitionistic fuzzy Hamacher general...

What does it mean to write an “efficient” theorem prover for first-order intuitionistic logic? This paper suggests a possible answer to the question, following the philosophy of logic programming. We decompose intuitionistic logic into two syntactically restricted subsets: (i) the class of simple embedded implications and (ii) the class of disjunctive and existential assertions. Each of these s...

The size of shortest cut-free proofs of first-order formulas in intuitionistic sequent calculus is known to be non-elementary in the worst case in terms of the size of given sequent proofs with cuts of the same formulas. In contrast to that fact, we provide an elementary bound for the size of cut-free proofs for disjunction-free intuitionistic logic for the case where the cut-formulas of the or...

A unified approach to the construction of original forms of the famous Herbrand theorem is suggested for first-order classical and intuitionistic logics without equality. It does not explore skolemization, have wording on deducibility, and as usual, makes the reduction of deducibility in the first-order logics to deducibility in their propositional fragments. The forms use the original notions ...

This paper introduces the intuitionistic rough set and intuitionistic rough relational and rough object oriented database models. Rough set, fuzzy set, and intuitionistic set uncertainty management are discussed and compared, and the model based on intuitionistic and rough sets developed here is applied to databases. The intuitionistic rough set database models draw benefits from both the rough...

In this paper the concept of intuitionistic fuzzy slightly precontinuous functions are introduced and studied. Intuitionistic fuzzy slightly precontinuity generalize intuitionistic fuzzy precontinuity. Besides giving characterizations and basic properties of this function, preservation theorems of intuitionistic fuzzy slightly precontinuous are also obtained. We also study relationships between...