Related papers: Satisfiability in {\L}ukasiewicz logic and its unb…
The Lambek calculus can be considered as a version of non-commutative intuitionistic linear logic. One of the interesting features of the Lambek calculus is the so-called "Lambek's restriction," that is, the antecedent of any provable…
Moisil logic, having as algebraic counterpart \L ukasiewicz-Moisil algebras, provide an alternative way to reason about vague information based on the following principle: a many-valued event is characterized by a family of Boolean events.…
Polyhedral semantics is a recently introduced branch of spatial modal logic, in which modal formulas are interpreted as piecewise linear subsets of an Euclidean space. Polyhedral semantics for the basic modal language has already been well…
We expand the notion of characteristic formula to infinite finitely presentable subdirectly irreducible algebras. We prove that there is a continuum of varieties of Heyting algebras containing infinite finitely presentable subdirectly…
Continuing to pursue a research direction that we already explored in connection with G\"odel-Dummett logic and Ruspini partitions, we show here that {\L}ukasiewicz logic is able to express the notion of pseudo-triangular basis of fuzzy…
We consider the one-variable fragment of first-order logic extended with Presburger constraints. The logic is designed in such a way that it subsumes the previously-known fragments extended with counting, modulo counting or cardinality…
We introduce infinitary action logic with exponentiation -- that is, the multiplicative-additive Lambek calculus extended with Kleene star and with a family of subexponential modalities, which allows some of the structural rules…
Inquisitive logic is a research program that extends the scope of logic to cover not only statements, but also questions. In the context of this program, a logic that plays a prominent role is inquisitive first-order logic, InqBQ, which…
Monadic second order logic and linear temporal logic are two logical formalisms that can be used to describe classes of infinite words, i.e., first-order models based on the natural numbers with order, successor, and finitely many unary…
We present new results on finite satisfiability of logics with counting and arithmetic. One result is a tight bound on the complexity of satisfiability of logics with so-called local Presburger quantifiers, which sum over neighbors of a…
The ordered structures of natural, integer, rational and real numbers are studied in this thesis. The theories of these numbers in the language of order are decidable and finitely axiomatizable. Also, their theories in the language of order…
We consider the logic MSO+U, which is monadic second-order logic extended with the unbounding quantifier. The unbounding quantifier is used to say that a property of finite sets holds for sets of arbitrarily large size. We prove that the…
Baaz's operator $\Delta$ was introduced (by Baaz) in order to extend G\"odel logics, after that this operator was used to expand fuzzy logics by H\'ajek in his celebrated book. These logics were called $\Delta$-fuzzy logics. On the other…
We give a syntactic characterization of abstract elementary classes (AECs) closed under intersections using a new logic with a quantifier for isomorphism types that we call structural logic: we prove that AECs with intersections correspond…
We combine the concepts of modal logics and many-valued logics in a general and comprehensive way. Namely, given any finite linearly ordered set of truth values and any set of propositional connectives defined by truth tables, we define the…
The framework of quantitative equational logic has been successfully applied to reason about algebras whose carriers are metric spaces and operations are nonexpansive. We extend this framework in two orthogonal directions: algebras endowed…
We present algebraic semantics for Continuous Propositional Logic, CPL, introduced by Itai Ben Yaacov, viewed as {\L}ukasiewicz propositional logic with a reversed truth-falsity orientation and enriched by a unary halving connective. We…
In this paper, three semilinear substructural logics ULw, IULw and HpsUL*w are constructed. Then the completeness of ULw and IULw with respect to classes of finite UL and IUL-algebras, respectively, is proved. Algebraically, non-integral…
We discuss the infinite dimensional algebras appearing in integrable perturbations of conformally invariant theories, with special emphasis in the structure of the consequent non-abelian infinite dimensional algebra generalizing $W_\infty$…
Classical logic predicts that everything (thus nothing useful at all) follows from inconsistency. A paraconsistent logic is a logic where an inconsistency does not lead to such an explosion, and since in practice consistency is difficult to…