Related papers: Some General Completeness Results for Propositiona…
Given a regular cardinal $\kappa$ such that $\kappa^{<\kappa}=\kappa$ (e.g., if the Generalized Continuum Hypothesis holds), we develop a proof system for classical infinitary logic that includes heterogeneous quantification (i.e., infinite…
Sequential propositional logic deviates from ordinary propositional logic by taking into account that during the sequential evaluation of a propositional statement,atomic propositions may yield different Boolean values at repeated…
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…
Modal fixpoint logics traditionally play a central role in computer science, in particular in artificial intelligence and concurrency. The mu-calculus and its relatives are among the most expressive logics of this type. However, popular…
In this chapter we survey two topics that have recently been investigated in frame theory. First, we give an overview of the class of scalable frames. These are (finite) frames with the property that each frame vector can be rescaled in…
We initiate the study of finite characterizations and exact learnability of modal languages. A finite characterization of a modal formula w.r.t. a set of formulas is a finite set of finite models (labelled either positive or negative) which…
We study preservation theorems for modal logics over finite structures with respect to three fundamental semantic relations: embeddings, injective homomorphisms, and homomorphisms. We focus on classes of pointed Kripke models that are…
Bernays introduced a method for proving underivability results in propositional calculi by truth tables. In general, this motivates an investigations of how to find, given a propositional logic, a finite-valued logic which has as few…
We say that a Kripke model is a GL-model if the accessibility relation $\prec$ is transitive and converse well-founded. We say that a Kripke model is a D-model if it is obtained by attaching infinitely many worlds $t_1, t_2, \ldots$, and…
Finiteness spaces constitute a categorical model of Linear Logic (LL) whose objects can be seen as linearly topologised spaces, (a class of topological vector spaces introduced by Lefschetz in 1942) and morphisms as continuous linear maps.…
We present a straightforward embedding of quantified multimodal logic in simple type theory and prove its soundness and completeness. Modal operators are replaced by quantification over a type of possible worlds. We present simple…
We prove a version of the finiteness conjecture for Kauffman bracket skein modules of $3$-manifolds with boundary, which was introduced by the second author in \cite{Det21}. In particular our methods, which are constructive, give an…
We consider the extension of two variable logic with quantifiers that state that the number of elements where a formula holds should belong to a given ultimately periodic set. We show that both satisfiability and finite satisfiability of…
Modal logic is a paradigm for several useful and applicable formal systems in computer science. It generally retains the low complexity of classical propositional logic, but notable exceptions exist in the domains of description, temporal,…
A theoretical framework bridging General Relativity (GR) and Quantum Dynamics (QD) is introduced through the application of Kripke semantics and linear logic. While conventional unification efforts often rely on structural or geometrical…
Coalgebras for a functor model different types of transition systems in a uniform way. This paper focuses on a uniform account of finitary logics for set-based coalgebras. In particular, a general construction of a logic from an arbitrary…
We find the model completion of the theory modules over $A$, where $A$ is a finitely generated commutative algebra over a field $K$. This is done in a context where the field $K$ and the module are represented by sorts in the theory, so…
In this paper, a new approximate syllogistic reasoning schema is described that expands some of the approaches expounded in the literature into two ways: (i) a number of different types of quantifiers (logical, absolute, proportional,…
In this paper we consider an approach where both propositions and the accessibility relation are infinitely many-valued over G\"{o}del algebras. In particular, we consider separately the $\Box $-fragment and the $\Diamond $-fragment of our…
A semantics is given to possibilistic logic, a logic that handles weighted classical logic formulae, and where weights are interpreted as lower bounds on degrees of certainty or possibility, in the sense of Zadeh's possibility theory. The…