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While reasoning in a logic extending a complete Boolean basis is coNP-hard, restricting to conjunctive fragments of modal languages sometimes allows for tractable reasoning even in the presence of greatest fixpoints. One such example is the…
Temporal logics are an obvious high-level descriptive companion formalism to dynamical systems which model behavior as deterministic evolution of state over time. A wide variety of distinct temporal logics applicable to dynamical systems…
Distributional semantics is the linguistic theory that a word's meaning can be derived from its distribution in natural language (i.e., its use). Language models are commonly viewed as an implementation of distributional semantics, as they…
This paper investigates the possibility of performing automated reasoning in probabilistic logic when probabilities are expressed by means of linguistic quantifiers. Each linguistic term is expressed as a prescribed interval of proportions.…
We develop and explore the idea of recognition of languages (in the general sense of subsets of topological algebras) as preimages of clopen sets under continuous homomorphisms into Stone topological algebras. We obtain an Eilenberg…
Our goal is to define an algebraic language for reasoning about non-deterministic computations. Towards this goal, we introduce an algebra of string-to-string transductions. Specifically, it is an algebra of partial functions on words over…
The principle behind algebraic language theory for various kinds of structures, such as words or trees, is to use a compositional function from the structures into a finite set. To talk about compositionality, one needs some way of…
Closely related languages show linguistic similarities that allow speakers of one language to understand speakers of another language without having actively learned it. Mutual intelligibility varies in degree and is typically tested in…
We propose a categorial grammar based on classical multiplicative linear logic. This can be seen as an extension of abstract categorial grammars (ACG) and is at least as expressive. However, constituents of {\it linear logic grammars (LLG)}…
We introduce a general categorical framework for the definition of weak behavioural equivalences, building on and extending recent results in the field. This framework is based on parametrized saturation categories, i.e. categories whose…
We establish a connection between measurement-based quantum computation and the field of mathematical logic. We show that the computational power of an important class of quantum states called graph states, representing resources for…
In the study of computational effects, it is important to consider the notion of computational effects with parameters. The need of such a notion arises when, for example, statically estimating the range of effects caused by a program, or…
Large language models (LLMs) demonstrate strong reasoning abilities in solving complex real-world problems. Yet, the internal mechanisms driving these complex reasoning behaviors remain opaque. Existing interpretability approaches targeting…
The classical Hennessy-Milner theorem says that two states of an image-finite transition system are bisimilar if and only if they satisfy the same formulas in a certain modal logic. In this paper we study this type of result in a general…
Game comonads provide a categorical syntax-free approach to finite model theory, and their Eilenberg-Moore coalgebras typically encode important combinatorial parameters of structures. In this paper, we develop a framework whereby the…
The belief construction is a fundamental technique for transforming partially observable systems to fully observable ones while preserving the relevant semantics. It plays a central role in the analysis of partially observable systems, in…
We present a non-deterministic semantic framework for all modal logics in the modal cube, extending prior works by Kearns and others. Our approach introduces modular and uniform multi-valued non-deterministic matrices (Nmatrices) for each…
Bialgebrae provide an abstract framework encompassing the semantics of different kinds of computational models. In this paper we propose a bialgebraic approach to the semantics of logic programming. Our methodology is to study logic…
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,…
The Eilenberg correspondence relates varieties of regular languages to pseudovarieties of finite monoids. Various modifications of this correspondence have been found with more general classes of regular languages on one hand and classes of…