A higher-order behavioural algebraic institution for ASL

In this paper, we generalise the semantics of ASL including the three behavioural operators for a fixed but arbitrary algebraic institution. After that, we define a behavioural algebraic institution which is used to give an alternative semantics of the behavioural operators, to define the normal forms of the both semantics of behavioural operators and to relate both semantics. Finally, we present a higher-order behavioural algebraic institution.Postprint (published version

A process-algebraic semantics for generalised nonblocking.

Generalised nonblocking is a weak liveness property to express the ability of a system to terminate under given preconditions. This paper studies the notions of equivalence and refinement that preserve generalised nonblocking and proposes a semantic model that characterises generalised nonblocking equivalence. The model can be constructed from the transition structure of an automaton, and has a finite representation for every finite-state automaton. It is used to construct a unique automaton representation for all generalised nonblocking equivalent automata. This gives rise to effective decision procedures to verify generalised nonblocking equivalence and refinement, and to a method to simplify automata while preserving generalised nonblocking equivalence. The results of this paper provide for better understanding of nonblocking in a compositional framework, with possible applications in compositional verification

An algebraic generalization of Kripke structures

The Kripke semantics of classical propositional normal modal logic is made algebraic via an embedding of Kripke structures into the larger class of pointed stably supported quantales. This algebraic semantics subsumes the traditional algebraic semantics based on lattices with unary operators, and it suggests natural interpretations of modal logic, of possible interest in the applications, in structures that arise in geometry and analysis, such as foliated manifolds and operator algebras, via topological groupoids and inverse semigroups. We study completeness properties of the quantale based semantics for the systems K, T, K4, S4, and S5, in particular obtaining an axiomatization for S5 which does not use negation or the modal necessity operator. As additional examples we describe intuitionistic propositional modal logic, the logic of programs PDL, and the ramified temporal logic CTL.Comment: 39 page

Categorical Abstract Algebraic Logic: Referential π-Institutions

Wójcicki introduced in the late 1970s the concept of a referential semantics for propositional logics. Referential semantics incorporate features of the Kripke possible world semantics for modal logics into the realm of algebraic and matrix semantics of arbitrary sentential logics. A well-known theorem of Wójcicki asserts that a logic has a referential semantics if and only if it is selfextensional. Referential semantics was subsequently studied in detail by Malinowski and the concept of selfextensionality has played, more recently, an important role in the field of abstract algebraic logic in connection with the operator approach to algebraizability. We introduce and review some of the basic definitions and results pertaining to the referential semantics of π-institutions, abstracting corresponding results from the realm of propositional logics

Semantics of a Typed Algebraic Lambda-Calculus

Algebraic lambda-calculi have been studied in various ways, but their semantics remain mostly untouched. In this paper we propose a semantic analysis of a general simply-typed lambda-calculus endowed with a structure of vector space. We sketch the relation with two established vectorial lambda-calculi. Then we study the problems arising from the addition of a fixed point combinator and how to modify the equational theory to solve them. We sketch an algebraic vectorial PCF and its possible denotational interpretations

Two Algebraic Process Semantics for Contextual Nets

We show that the so-called 'Petri nets are monoids' approach initiated by Meseguer and Montanari can be extended from ordinary place/transition Petri nets to contextual nets by considering suitable non-free monoids of places. The algebraic characterizations of net concurrent computations we provide cover both the collective and the individual token philosophy, uniformly along the two interpretations, and coincide with the classical proposals for place/transition Petri nets in the absence of read-arcs