78 research outputs found
A semantics and a logic for Fuzzy Arden Syntax
Fuzzy programming languages, such as the Fuzzy Arden Syntax (FAS), are used to describe behaviours which evolve in a fuzzy way and thus cannot be characterized neither by a Boolean outcome nor by a probability distribution. This paper introduces a semantics for FAS, focusing on the weighted parallel interpretation of its conditional statement. The proposed construction is based on the notion of a fuzzy multirelation which associates with each state in a program a fuzzy set of weighted possible evolutions. The latter is parametric on a residuated lattice which models the underlying semantic ‘truth space’. Finally, a family of dynamic logics, equally parametric on the residuated lattice, is introduced to reason about FAS programsThis work was founded by the ERDF — European Regional Development Fund through the Operational Programme for Competitiveness and Internationalisation — COMPETE 2020 Pro gramme and by National Funds through the Portuguese funding agency, FCT — Fundação para a Ciência e a Tecnologia, within projects
POCI-01-0145-FEDER-030947and POCI-01-0145-FEDER-02994
The Structure of First-Order Causality
Game semantics describe the interactive behavior of proofs by interpreting
formulas as games on which proofs induce strategies. Such a semantics is
introduced here for capturing dependencies induced by quantifications in
first-order propositional logic. One of the main difficulties that has to be
faced during the elaboration of this kind of semantics is to characterize
definable strategies, that is strategies which actually behave like a proof.
This is usually done by restricting the model to strategies satisfying subtle
combinatorial conditions, whose preservation under composition is often
difficult to show. Here, we present an original methodology to achieve this
task, which requires to combine advanced tools from game semantics, rewriting
theory and categorical algebra. We introduce a diagrammatic presentation of the
monoidal category of definable strategies of our model, by the means of
generators and relations: those strategies can be generated from a finite set
of atomic strategies and the equality between strategies admits a finite
axiomatization, this equational structure corresponding to a polarized
variation of the notion of bialgebra. This work thus bridges algebra and
denotational semantics in order to reveal the structure of dependencies induced
by first-order quantifiers, and lays the foundations for a mechanized analysis
of causality in programming languages
Hoare Semigroups
A semigroup-based setting for developing Hoare logics and refinement calculi is introduced together with procedures for translating between verification and refinement proofs. A new Hoare logic for multirelations and two minimalist generic verification and refinement components, implemented in an interactive theorem prover, are presented as applications that benefit from this generalisation
Nets, relations and linking diagrams
In recent work, the author and others have studied compositional algebras of
Petri nets. Here we consider mathematical aspects of the pure linking algebras
that underly them. We characterise composition of nets without places as the
composition of spans over appropriate categories of relations, and study the
underlying algebraic structures.Comment: 15 pages, Proceedings of 5th Conference on Algebra and Coalgebra in
Computer Science (CALCO), Warsaw, Poland, 3-6 September 201
Presentation of a Game Semantics for First-Order Propositional Logic
Game semantics aim at describing the interactive behaviour of proofs by
interpreting formulas as games on which proofs induce strategies. In this
article, we introduce a game semantics for a fragment of first order
propositional logic. One of the main difficulties that has to be faced when
constructing such semantics is to make them precise by characterizing definable
strategies - that is strategies which actually behave like a proof. This
characterization is usually done by restricting to the model to strategies
satisfying subtle combinatory conditions such as innocence, whose preservation
under composition is often difficult to show. Here, we present an original
methodology to achieve this task which requires to combine tools from game
semantics, rewriting theory and categorical algebra. We introduce a
diagrammatic presentation of definable strategies by the means of generators
and relations: those strategies can be generated from a finite set of
``atomic'' strategies and that the equality between strategies generated in
such a way admits a finite axiomatization. These generators satisfy laws which
are a variation of bialgebras laws, thus bridging algebra and denotational
semantics in a clean and unexpected way
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