Completeness and Cut-elimination in the Intuitionistic Theory of Types

Draft Completeness and Cut-elimination in the Intuitionistic Theory of Types

In this paper we give a semantic proof of cut-elimination for ICTT. ICTT is an intuitionistic formulation of Church’s theory of types defined by Miller, Scedrov, Nadathur and Pfenning in the late 1980s. It is the basis for the λprolog programming language. Our approach, extending techniques of Takahashi, Andrews and tableaux machinery of Fitting, Smullyan, Nerode and Shore, is to prove a comple...

Completeness and Cut-elimination in the Intuitionistic Theory of Types - Part 2

SOME RESULTS ON INTUITIONISTIC FUZZY SPACES

In this paper we define intuitionistic fuzzy metric and normedspaces. We first consider finite dimensional intuitionistic fuzzy normed spacesand prove several theorems about completeness, compactness and weak convergencein these spaces. In section 3 we define the intuitionistic fuzzy quotientnorm and study completeness and review some fundamental theorems. Finally,we consider some properties of...

Semantic Cut Elimination in the Intuitionistic Sequent Calculus

Cut elimination is a central result of the proof theory. This paper proposes a new approach for proving the theorem for Gentzen’s intuitionistic sequent calculus LJ, that relies on completeness of the cutfree calculus with respect to Kripke Models. The proof defines a general framework to extend the cut elimination result to other intuitionistic deduction systems, in particular to deduction mod...

Extended Abstract: Reconsidering Intuitionistic Duality

This paper proposes a new syntax and proof system called Dualized Intuitionistic Logic (DIL), for intuitionistic propositional logic with the subtraction operator. Our goal is a conservative extension of standard propositional intuitionistic logic with perfect duality (symmetry) between positive and negative connectives. The proof system should satisfy the following metatheoretic properties: so...