In the paper we introduce logical calculi for representation of propositions with modal operators indexed by fuzzy values. There calculi are called Heyting-valued modal logics. We introduce the concept of a Heyting-valued Kripke model and consider a semantics of Heyting-valued modal logics at the class of Heyting-valued Kripke models.

Like in the case of classical logic and other non-standard logics, a variety of complexity-related questions can be asked in the context of many-valued logic. Some questions, such as the complexity of the sets of satisfiable and valid formulas in various logics, are completely standard; others, such as the maximal size of representations of many-valued connectives, only make sense in a many-val...

Maximality is a desirable property of paraconsistent logics, motivated by the aspiration to tolerate inconsistencies, but at the same time retain from classical logic as much as possible. In this paper, we introduce the strongest possible notion of maximal paraconsistency, and investigate it in the context of logics that are based on deterministic or non-deterministic three-valued matrices. We ...

A classical Gentzen-type system is one which employs two-sided sequents, together with structural and logical rules of a certain characteristic form. A decent Gentzentype system should allow for direct proofs, which means that it should admit some useful forms of cut elimination and the subformula property. In this tutorial we explain the main difficulty in developing classical Gentzen-type sys...

We describe the automated theorem prover \Deep Thought" (d DT). The prover can be used for arbitrary multiple-valued rst-order logics, provided the connec-tives can be deened by truth tables and the quantiiers are generalizations of the classical universal resp. ex-istential quantiiers. d DT has been tested with many interesting multiple-valued logics as well as classical rst-order predicate lo...

DeWitt, Richard. 2005. On retaining classical truths and classical deducibility in many-valued and fuzzy logics. DeWitt, Richard, "On retaining classical truths and classical deducibility in many-valued and fuzzy logics" (2005). Philosophy Faculty Publications. Paper 3.