in this paper we continue development of formal theory of a special class offuzzy logics, called eq-logics. unlike fuzzy logics being extensions of themtl-logic in which the basic connective is implication, the basic connective ineq-logics is equivalence. therefore, a new algebra of truth values calledeq-algebra was developed. this is a lower semilattice with top element endowed with two binary...

In the paper by Oscar Estrada et al. it is introduced the concept of “Possibilistic Intuitionistic Logic (PIL)”; In that paper, the authors present results analogous to those of the well-known intuitionistic logic, such as a Deduction Theorem, a Generalized version of the Deduction Theorem, a Cut Rule, a weak version of a Refutation Theorem, a Substitution Theorem and Glivenko’s Theorem. The co...

In this paper, we shortly review two formal approaches in verification of security protocols; model checking and theorem proving. Model checking is based on studying the behavior of protocols via generating all different behaviors of a protocol and checking whether the desired goals are satisfied in all instances or not. We investigate Scyther operational semantics as n example of this...

A calculus of typed relations subsuming the classical relational database theory is presented. An associated sound and complete deduction mechanism is developed. The formulation is generalized to deal with nondeterministic databases and information relations in the rough set-style. keywords: relational logic, typed relations, relational database, nondeterministic databases, information relation...

Birkhoff’s completeness theorem of equational logic asserts the coincidence of the model-theoretic and proof-theoretic consequence relations. Goguen and Meseguer, giving a sound and adequate system of inference rules for finitary many-sorted equational deduction, generalized the completeness theorem of Birkhoff to the completeness of finitary many-sorted equational logic and provided simultaneo...

In a system of sequents for intuitionistic predicate logic a theorem, which corresponds to Prawitz’s Normal Form Theorem for natural deduction, are proved. In sequent derivations a special kind of cuts, maximum cuts, are defined. Maximum cuts from sequent derivations are connected with maximum segments from natural deduction derivations, i.e., sequent derivations without maximum cuts correspond...

Modern software systems usually deal with several sorts (types) of data elements simultaneously. Some of these sorts, like integers, booleans, and so on, can be seen as having an immediate, direct nature and therefore are called visible, and they are contrasted with the others, like types of objects (in OO sense), which are called hidden sorts. A language used to specify such software system ha...

Various sources in the literature claim that the deduction theorem does not hold for normal modal or epistemic logic, whereas others present versions of the deduction theorem for several normal modal systems. It is shown here that the apparent problem arises from an objectionable notion of derivability from assumptions in an axiomatic system. When a traditional Hilbert-type system of axiomatic ...