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Bialgebraic Semantics for Logic Programming

Filippo Bonchi ; Fabio Zanasi.

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 programs as reactive systems and exploit abstract techniques&nbsp;[&hellip;]

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Coalgebraic Semantics for Probabilistic Logic Programming

Tao Gu ; Fabio Zanasi.

Probabilistic logic programming is increasingly important in artificial intelligence and related fields as a formalism to reason about uncertainty. It generalises logic programming with the possibility of annotating clauses with probabilities. This paper proposes a coalgebraic semantics on&nbsp;[&hellip;]

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Universal Constructions for (Co)Relations: categories, monoidal categories, and props

Brendan Fong ; Fabio Zanasi.

Calculi of string diagrams are increasingly used to present the syntax and algebraic structure of various families of circuits, including signal flow graphs, electrical circuits and quantum processes. In many such approaches, the semantic interpretation for diagrams is given in terms of relations or&nbsp;[&hellip;]

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Equivalence checking for weak bi-Kleene algebra

Tobias Kappé ; Paul Brunet ; Bas Luttik ; Alexandra Silva ; Fabio Zanasi.

Pomset automata are an operational model of weak bi-Kleene algebra, which describes programs that can fork an execution into parallel threads, upon completion of which execution can join to resume as a single thread. We characterize a fragment of pomset automata that admits a decision procedure for&nbsp;[&hellip;]

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A Finite Axiomatisation of Finite-State Automata Using String Diagrams

Robin Piedeleu ; Fabio Zanasi.

We develop a fully diagrammatic approach to finite-state automata, based on reinterpreting their usual state-transition graphical representation as a two-dimensional syntax of string diagrams. In this setting, we are able to provide a complete equational theory for language equivalence, with two&nbsp;[&hellip;]

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String diagrams for Strictification and Coherence

Paul Wilson ; Dan Ghica ; Fabio Zanasi.

Whereas string diagrams for strict monoidal categories are well understood, and have found application in several fields of Computer Science, graphical formalisms for non-strict monoidal categories are far less studied. In this paper, we provide a presentation by generators and relations of string&nbsp;[&hellip;]

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