On strengthening intuitionistic logic.

On not strengthening intuitionistic logic

We wish to reexamine —in the wake of R. E. Vesley's Γ7] —the question of converting so-called structural and intelim rules for PC/, the intuitionistic sequenzen-kalkύl of Gentzen, into rules for PCc, the classical sequenzenkalkίil. We shall limit ourselves here to sequenzen or turnstile statements of the form Al9 A2, . . . , An h B, where Au A2, . . . , An, (n s* 0), and B are wff s consisting ...

On an Intuitionistic Modal Logic

In this paper we consider an intuitionistic variant of the modal logic S4 (which we call IS4). The novelty of this paper is that we place particular importance on the natural deduction formulation of IS4—our formulation has several important metatheoretic properties. In addition, we study models of IS4, not in the framework of Kripke semantics, but in the more general framework of category theo...

Intuitionistic Logic

There are basically two ways to view intuitionistic logic: (i) as a philosoph ical–foundational issue in mathematics, (ii) as a technical discipline within mathematical logic. Let us deal with the philosophical aspects first, they will provide the motivation for the subject. In doing so, we will follow L.E.J. Brouwer, the founding father of intuitionism. Brouwer did contribute little to intuiti...

AN ALGEBRAIC STRUCTURE FOR INTUITIONISTIC FUZZY LOGIC

In this paper we extend the notion of  degrees of membership and non-membership of intuitionistic fuzzy sets to lattices and  introduce a residuated lattice with appropriate operations to serve as semantics of intuitionistic fuzzy logic. It would be a step forward to find an algebraic counterpart for intuitionistic fuzzy logic. We give the main properties of the operations defined and prove som...

Semantical Observations on the Embedding of Intuitionistic Logic into Intuitionistic Linear Logic