相关论文: Monadic BL-algebras: the equivalent algebraic sema…

The notion of orbit finite data monoid was recently introduced by Bojanczyk as an algebraic object for defining recognizable languages of data words. Following Buchi's approach, we introduce a variant of monadic second-order logic with data…

Unbounded {\L}ukasiewicz logic is a substructural logic that combines features of infinite-valued {\L}ukasiewicz logic with those of abelian logic. The logic is finitely strongly complete w.r.t.~the additive $\ell$-group on the reals…

We present a coalgebraic generalisation of Fischer and Ladner's Propositional Dynamic Logic (PDL) and Parikh's Game Logic (GL). In earlier work, we proved a generic strong completeness result for coalgebraic dynamic logics without…

We show that over the class of linear orders with additional binary relations satisfying some monotonicity conditions, monadic first-order logic has the three-variable property. This generalizes (and gives a new proof of) several known…

Two decades ago P. Martin and D. Woodcock made a surprising and prophetic link between statistical mechanics and representation theory. They observed that the decomposition numbers of the blob algebra (that appeared in the context of…

Usually a name of the category is inherited from the name of objects. However more relevant for a category of objects and morphisms is an algebra of morphisms. Therefore we prefer to say a category of graphs if every morphism is a graph. In…

The aim of this paper is to show that even if the natural algebraic semantic for modal (normal) logic is modal algebra, the more general class of subordination algebras (roughly speaking, the non symmetric contact algebras) is adequate too…

The one-variable fragment of any first-order logic may be considered as a modal logic, where the universal and existential quantifiers are replaced by a box and diamond modality, respectively. In several cases, axiomatizations of algebraic…

Algebraic logic studies algebraic theories related to proposition and first-order logic. A new algebraic approach to first-order logic is sketched in this paper. We introduce the notion of a quantifier theory, which is a functor from the…

In this note, we study various relational and algebraic aspects of the bounded quasi-implication algebras introduced by Hardegree. By generalizing the constructions given by MacLaren and Goldblatt within the setting of ortholattices, we…

This paper aims at connecting the various classes that provide an algebraic semantics for three different conservative expansions of Lukasiewicz logic, using algebraic and category-theoretical techniques. We connect such classes of algebras…

Generalizing standard monadic second-order logic for Kripke models, we introduce monadic second-order logic interpreted over coalgebras for an arbitrary set functor. Similar to well-known results for monadic second-order logic over trees,…

In this paper, we introduce the subvariety of quasi-MV* algebras in order to characterize the logic which is related to complex fuzzy logic. First, we give the definitions of strong quasi-MV* algebra and strong quasi-Wajsberg* algebra and…

We study the S5-modal expansion of the logic based on the Lukasiewicz t-norm. We exhibit a finitary propositional calculus and show that it is finitely strongly complete with respect to this logic. This propositional calculus is then…

One of the main reasons for the correspondence of regular languages and monadic second-order logic is that the class of regular languages is closed under images of surjective letter-to-letter homomorphisms. This closure property holds for…

The logarithmic Kazhdan-Lusztig correspondence is a conjectural equivalence between braided tensor categories of representations of small quantum groups and representations of certain vertex operator algebras. In this article we prove such…

Monadic second order logic is the expansion of first order logic by quantifiers ranging over unary relations. We study the shared monadic second order theory of finite linear orders, i.e. the pseudofinite monadic second order theory of…

We present two embeddings of infinite-valued Lukasiewicz logic L into Meyer and Slaney's abelian logic A, the logic of lattice-ordered abelian groups. We give new analytic proof systems for A and use the embeddings to derive corresponding…

Modal probabilistic logics provide a framework for reasoning about probability in modal contexts, involving notions such as knowledge, belief, time, and action. In this paper, we study a particular family of these logics, extending the…

Fuzzy logic extends the classical truth values "true" and "false" with additional truth degrees in between. More specifically, fuzzy modal logics in this sense are given by a choice of fuzzy modalities and a fuzzy propositional base. It has…