Related papers: Logic Column 15: Coalgebras and Their Logics
We describe various strengthenings of the concept of topological transitivity. Especially when one departs from the family of invertible systems, a number of interesting properties arise. We present the architecture of implications among…
We investigate dynamic reconfigurable component-based systems whose architectures are described by formulas of Propositional Configuration Logics. We present several examples of reconfigurable systems based on well-known architectures, and…
Interconnected dynamic systems are a pervasive component of our modern infrastructures. The complexity of such systems can be staggering, which motivates simplified representations for their manipulation and analysis. This work introduces…
We study rational streams (over a field) from a coalgebraic perspective. Exploiting the finality of the set of streams, we present an elementary and uniform proof of the equivalence of four notions of representability of rational streams:…
This paper proposes to use dialgebras to specify the semantics of interactive systems in a natural way. Dialgebras are a conservative extension of coalgebras. In this categorical model, from the point of view that we provide, the notions of…
Compositionality is a key property for dealing with complexity, which has been studied from many points of view in diverse fields. Particularly, the composition of individual computations (or programs) has been widely studied almost since…
We present a comprehensive programme analysing the decomposition of proof systems for non-classical logics into proof systems for other logics, especially classical logic, using an algebra of constraints. That is, one recovers a proof…
In the present paper, we describe some experiences in using programming, commands and graphical interfaces based on computer algebra systems, as tools for learning Physics and Mathematics.
We introduce a new family of temporal logics designed to finely balance the trade-off between expressivity and complexity. Their key feature is the possibility of defining operators of a new kind that we call transformation operators. Some…
Most of the engineering and physical systems are generally characterized by differential and difference equations based on their continuous-time and discrete-time dynamics, respectively. Moreover, these dynamical models are analyzed using…
In this note, we observe a relation between dialgebras (in particular, Leibniz algebras) and conformal algebras. The purpose is to show how the methods of conformal algebras help solving problems on dialgebras, and, conversely, how the…
We present a form of algebraic reasoning for computational objects which are expressed as graphs. Edges describe the flow of data between primitive operations which are represented by vertices. These graphs have an interface made of…
Computational studies of basic models of strongly-correlated electron systems can provide guidance in the search for new materials as well as insight into the physical mechanisms responsible for their properties. Here, we illustrate this by…
This paper is a brief and informal presentation of cirquent calculus, a novel proof system for resource-conscious logics. As such, it is a refinement of sequent calculus with mechanisms that allow to explicitly account for the possibility…
We bring forward a logical system of transition algebras that enhances many-sorted first-order logic using features from dynamic logics. The sentences we consider include compositions, unions, and transitive closures of transition…
The paper is devoted to the introduction of natural deduction systems for some weak subintuitionistic logics, along with proofs of normalization theorems for these systems.
Reachability Logic is a formalism that can be used, among others, for expressing partial-correctness properties of transition systems. In this paper we present three proof systems for this formalism, all of which are sound and complete and…
In order to combine operational and logical styles of specifications in one unified framework, the notion of logic labelled transition systems (Logic LTS, for short) has been presented and explored by L\"{u}ttgen and Vogler in [TCS…
A thorough investigation of the foundations of paraconsistent logics. Relations between logical principles are formally studied, a novel notion of consistency is introduced, the logics of formal inconsistency, and the subclasses of…
In this article we investigate the notion and basic properties of Boolean algebras and prove the Stone's representation theorem. The relations of Boolean algebras to logic and to set theory will be studied and, in particular, a neat proof…