Related papers: Towards a Higher-Order Bialgebraic Denotational Se…
In Apt and Bezem [AB99] (see cs.LO/9811017) we provided a computational interpretation of first-order formulas over arbitrary interpretations. Here we complement this work by introducing a denotational semantics for first-order logic.…
The foundational concepts of semantic numeration systems theory are briefly outlined. The action of cardinal semantic operators unfolds over a set of cardinal abstract entities belonging to the cardinal semantic multeity. The cardinal…
One of the basic sanity properties of a behavioural semantics is that it constitutes a congruence with respect to standard process operators. This issue has been traditionally addressed by the development of rule formats for transition…
The paper is a contribution both to the theoretical foundations and to the actual construction of efficient automatizable proof procedures for non-classical logics. We focus here on the case of finite-valued logics, and exhibit: (i) a…
This paper connects a vector-based composition model to a formal semantics, the Dependency-based Compositional Semantics (DCS). We show theoretical evidence that the vector compositions in our model conform to the logic of DCS.…
It is possible to translate a modified version of K. Worytkiewicz's combinatorial semantics of CCS (Milner's Calculus of Communicating Systems) in terms of labelled precubical sets into a categorical semantics of CCS in terms of labelled…
State-of-the-art Datalog engines include expressive features such as ADTs (structured heap values), stratified aggregation and negation, various primitive operations, and the opportunity for further extension using FFIs. Current…
We propose an operationally-based deductive proof method for program equivalence. It is based on encoding the language semantics as logically constrained term rewriting systems (LCTRSs) and the two programs as terms. The main feature of our…
One of the fundamental requirements for models of semantic processing in dialogue is incrementality: a model must reflect how people interpret and generate language at least on a word-by-word basis, and handle phenomena such as fragments,…
Developing suitable formal semantics can be of great help in the understanding, design and implementation of a programming language, and act as a guide for software development tools like analyzers or partial evaluators. In this sense, full…
Combining higher-order abstract syntax and (co)induction in a logical framework is well known to be problematic. Previous work described the implementation of a tool called Hybrid, within Isabelle HOL, which aims to address many of these…
The logical parallelism of propositional connectives and type constructors extends beyond the static realm of predicates, to the dynamic realm of processes. Understanding the logical parallelism of process propositions and dynamic types was…
In this paper we provide an alternative semantics for Equilibrium Logic and its monotonic basis, the logic of Here-and-There (also known as G\"odel's G3 logic) that relies on the idea of "denotation" of a formula, that is, a function that…
I present a formal connection between algebraic effects and game semantics, two important lines of work in programming languages semantics with applications in compositional software verification. Specifically, the algebraic signature…
Indexed languages are a classical notion in formal language theory, which has attracted attention in recent decades due to its role in higher-order model checking: They are precisely the languages accepted by order-2 pushdown automata. The…
The book is devoted to two research areas: (1) Designing programming languages along with their denotational models. A denotational model of a language consists of two many-sorted algebras - an algebra of syntax and an algebra of…
In recent years, optimization theory has been greatly impacted by the advent of sum of squares (SOS) optimization. The reliance of this technique on large-scale semidefinite programs however, has limited the scale of problems to which it…
Algebraic theories with dependency between sorts form the structural core of Martin-L\"of type theory and similar systems. Their denotational semantics are typically studied using categorical techniques; many different categorical…
We propose a deep semantic characterization of space and motion categorically from the viewpoint of grounding embodied human-object interactions. Our key focus is on an ontological model that would be adept to formalisation from the…
What makes two computational systems equivalent? Topos theory answers with classifying toposes: a system's semantic content is encoded in the geometric theory it classifies, and two presentations are equivalent when their classifying…