We introduce a suitable notion of bisimulation for the family of Heyting-valued modal logics introduced by M. Fitting. In this family of logics, each modal language is built on an underlying space of truth values, a Heyting algebra H. All the truth values are directly represented in the language which is interpreted on relational frames with an H-valued accessibility relation. We prove that for...

Axiomatizability, the finite model property (FMP), and decidability are some of the most frequently studied properties of non-classical logics. One of the first general methods of axiomatizing large classes of superintuitionistic logics (si-logics for short) was developed by Jankov [8]. For each finite subdirectly irreducible Heyting algebra A, Jankov designed a formula that encodes the structu...

We examine the notion of bisimulation and its ramifications, in the context of the family of Heyting-valued modal languages introduced by M. Fitting. Each modal language in this family is built on an underlying space of truth values, a Heyting algebra H. All the truth values are directly represented in the language, which is interpreted on relational frames with an H-valued accessibility relati...

(6) For every finite element a of V→̇C holds {a} ∈ SubstitutionSet(V,C). (7) If A a B = A, then for every set a such that a ∈ A there exists a set b such that b ∈ B and b⊆ a. (8) If μ(A a B) = A, then for every set a such that a ∈ A there exists a set b such that b ∈ B and b⊆ a. (9) If for every set a such that a ∈ A there exists a set b such that b ∈ B and b ⊆ a, then μ(A a B) = A. Let V be a s...

In this paper we define and examine frame constructions for the family of many-valued modal logics introduced by M. Fitting in the ’90s. Every language of this family is built on an underlying space of truth values, a Heyting algebra H. We generalize Fitting’s original work by considering complete Heyting algebras as truth spaces and proceed to define a suitable notion of H-indexed families of ...

EQ-algebras were introduced by Novak (2006) as an algebraic structure of truth values for fuzzy-type theory (FFT). Novák and De Baets (2009) various kinds such good, residuated, IEQ-algebras. In this paper, we define the notion (pre)ideal in bounded (BEQ-algebras) investigate some properties. Then, introduce a congruence relation on good BEQ-algebras using ideals, then, solve open problem Paad ...

In Coecke (2002a) we proposed the intuitionistic or disjunctive representation of quantum logic, i.e., a representation of the property lattice of physical systems as a complete Heyting algebra of logical propositions on these properties, where this complete Heyting algebra goes equipped with an additional operation, the operational resolution, which identifies the properties within the logic o...

Sheaves of structures are useful to give constructions in universal algebra and model theory. We can describe their logical behavior terms Heyting-valued structures. In this paper, we first provide a systematic treatment sheaves from the viewpoint categorical logic. then prove form {\L}o\'s's theorem for also characterization which holds with respect any maximal filter.

this paper provides a review on major ergodic features of semi-independent hyper mv {algebra dynamical systems. theorems are presentedto make contribution to calculate the entropy. particularly, it is proved that thetotal entropy of those semi-independent hyper mv {algebra dynamical systemsthat have a generator can be calculated with respect to their generator ratherthan considering all the par...