Related papers: Logic Column 15: Coalgebras and Their Logics
In this article we determine several theorems and methods for solving linear congruences and systems of linear congruences, and we find the number of distinct solutions. Many examples of solving congruences are given.
The paper presents algebraic and logical developments. From the algebraic viewpoint, we introduce Monadic Equational Systems as an abstract enriched notion of equational presentation. From the logical viewpoint, we provide Equational…
Consistency properties of concurrent computations, e.g., sequential consistency, linearizability, or eventual consistency, are essential for devising correct concurrent algorithms. In this paper, we present a logical formalization of such…
Coalgebras for a functor model different types of transition systems in a uniform way. This paper focuses on a uniform account of finitary logics for set-based coalgebras. In particular, a general construction of a logic from an arbitrary…
The foundational character of certain algebraic structures as Boolean algebras and Heyting algebras is rooted in their potential to model classical and constructive logic, respectively. In this paper we discuss the contributions of…
Dynamical systems are abstract models of interaction between space and time. They are often used in fields such as physics and engineering to understand complex processes, but due to their general nature, they have found applications for…
The paper presents an extension of temporal epistemic logic with operators that quantify over strategies. The language also provides a natural way to represent what agents would know were they to be aware of the strategies being used by…
We provide a compositional coalgebraic semantics for strategic games. In our framework, like in the semantics of functional programming languages, coalgebras represent the observable behaviour of systems derived from the behaviour of the…
The standard assumptions that underlie many conceptual and quantitative frameworks do not hold for many complex physical, biological, and social systems. Complex systems science clarifies when and why such assumptions fail and provides…
The identification and classification of phases in small systems, e.g. nuclei, social and financial networks, clusters, and biological systems, where the traditional definitions of phase transitions are not applicable, is important to…
We give a brief introduction to the mode-coupling theory of the glass transition, a theory which was proposed a while ago to describe the dynamics of supercooled liquids. After presenting the basic equations of the theory, we review some of…
This paper provides a preparatory introduction to torsors, written with a view toward later applications in the author's work. Rather than aiming at a comprehensive survey, the exposition focuses on those aspects of torsors that are most…
These lectures given to graduate students in theoretical particle physics, provide an introduction to the ``inner workings'' of computer algebra systems. Computer algebra has become an indispensable tool for precision calculations in…
An algebraic method is used to study the semantics of exceptions in computer languages. The exceptions form a computational effect, in the sense that there is an apparent mismatch between the syntax of exceptions and their intended…
The aim of this paper is to propose an alternative behavioural definition of computation (and of a computer) based simply on whether a system is capable of reacting to the environment-the input-as reflected in a measure of programmability.…
Logic has its origins in basic questions about the nature of the real world and how we describe it. This article seeks to bring out the physical and epistemological relevance of some of the more recent technical work in logic and…
The intransitive cycle of superiority is characterized by such binary relations between A, B, and C that A is superior to B, B is superior to C, and C is superior to A (i.e., A>B>C>A - in contrast with transitive relations A>B>C). The first…
A short introduction to the mathematical methods and technics of differential algebras and modules adapted to the problems of mathematical and theoretical physics is presented.
By a physical system we recognize a set of propositions about a given system with their truth-values depending on the states of the system. Since every physical system can go from one state in another one, there exists a binary relation on…
A logic is presented for reasoning on iterated sequences of formulae over some given base language. The considered sequences, or "schemata", are defined inductively, on some algebraic structure (for instance the natural numbers, the lists,…