We present a first order formula characterizing the distributive lattices L whose Priestley spaces P(L) contain no copy of a finite forest T . For Heyting algebras L, prohibiting a finite poset T in P(L) is characterized by equations iff T is a tree. We also give a condition characterizing the distributive lattices whose Priestley spaces contain no copy of a finite forest with a single addition...

A bottom–up investigation of algebraic structures corresponding to many valued logical systems is made. Particular attention is given to the unit interval as a prototypical model of these kind of structures. At the top level of our construction, Heyting Wajsberg algebras are defined and studied. The peculiarity of this algebra is the presence of two implications as primitive operators. This cha...

In the present paper, we study fuzzy multimodal logics over complete Heyting algebras and Kripke models for these logics. We introduce two types of simulations (forward backward) five bisimulations (forward, backward, forward-backward, backward-forward regular) between models, as well corresponding presimulations prebisimulations, which are with relaxed conditions. For each type an efficient al...

In AI and other branches of Computer Science expert models are often studied and used. Here we examine experts which evaluate formulas of modal logic. An expert model consists of a set of experts and a domination relation which dictates how each expert’s opinion is dependent upon the opinions expressed by other experts. Such multiple-expert modal models were introduced and investigated by Fitti...

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 ...

We extend the lattice embedding of the axiomatic extensions of the positive fragment of intuitionistic logic into the axiomatic extensions of intuitionistic logic to the setting of substructural logics. Our approach is algebraic and uses residuated lattices, the algebraic models for substructural logics. We generalize the notion of the ordinal sum of two residuated lattices and use it to obtain...

We develop the mathematical theory of epistemic updates with the tools of duality theory. We focus on the Logic of Epistemic Actions and Knowledge (EAK), introduced by Baltag-MossSolecki, without the common knowledge operator. We dually characterize the product update construction of EAK as a certain construction transforming the complex algebras associated with the given model into the complex...

We develop a symmetric analog of brace algebras and discuss the relation of such algebras to L∞-algebras. We then explain how these symmetric brace algebras may be used to examine the L∞-algebras that result from a particular gauge theory for massless particles of high spin.

In this paper, we investigate more relations between the symmetric residuated lattices $L$ with their corresponding intuitionistic fuzzy residuated lattice $tilde{L}$. It is shown that some algebraic structures of $L$ such as Heyting algebra, Glivenko residuated lattice and strict residuated lattice are preserved for $tilde{L}$. Examples are given for those structures that do not remain the sam...