Related papers: Symbolic dynamics and semigroup theory
Partial dynamical systems (X,alpha) arise naturally when dealing with commutative C*-dynamical system (A,delta). We associate with every pair (X,alpha), or (A,delta), a covariance C*-algebra C*(X,alpha)=C*(A,delta) which agrees with a…
Designers of autonomous agents, whether in physical or virtual environments, need to express nondeterminisim, failure, and parallelism in behaviors, as well as accounting for synchronous coordination between agents. Behavior Trees are a…
Giving a formal semantic to an UML Activity diagram (UML AD) is a hard task. The reason of this difficulty is the ambiguity and the absence of a precise formal semantic of such semi-formal formalism. A variety of semantics exist in the…
Calculi of string diagrams are increasingly used to present the syntax and algebraic structure of various families of circuits, including signal flow graphs, electrical circuits and quantum processes. In many such approaches, the semantic…
The study and understanding of human behaviour is relevant to computer science, artificial intelligence, neural computation, cognitive science, philosophy, psychology, and several other areas. Presupposing cognition as basis of behaviour,…
In this paper we provide a closed mathematical formulation of our previous results in the field of symbolic dynamics of unimodal maps. This being the case, we discuss the classical theory of applied symbolic dynamics for unimodal maps and…
Motivated by intuitive properties of physical quantities, the notion of a non-anomalous semigroup is formulated. These are totally ordered semigroups where there are no `infinitesimally close' elements. The real numbers are then defined as…
We introduce an algebraic structure which encodes a collection of countable graphs through a set of states, generators and relations. These structures, which we call blueprints, can capture standard algebraic objects such as groups, monoids…
Emergent collective group processes and capabilities have been studied through analysis of transactive memory, measures of group task performance, and group intelligence, among others. In their approach to collective behaviors, these…
We revisit the behavioral approach to systems theory and make explicit the abstract pattern that governs it. Our end goal is to use that pattern to understand interaction-related phenomena that emerge when systems interact. Rather than…
A prototype for an extensible interactive graphical term manipulation system is presented that combines pattern matching and nondeterministic evaluation to provide a convenient framework for doing tedious algebraic manipulations that so far…
Natural language and visualization are being increasingly deployed together for supporting data analysis in different ways, from multimodal interaction to enriched data summaries and insights. Yet, researchers still lack systematic…
Humans often employ figurative language use in communication, including during interactions with dialog systems. Thus, it is important for real-world dialog systems to be able to handle popular figurative language constructs like metaphor…
This article is devoted to the tactical game theoretical interpretation of dialectics. Dialectical games are considered as abstractly as well as models of the internal dialogue and reflection. The models related to the representation theory…
Symbolic models are abstract descriptions of continuous systems in which symbols represent aggregates of continuous states. In the last few years there has been a growing interest in the use of symbolic models as a tool for mitigating…
Symbol grounding (Harnad, 1990) describes how symbols such as words acquire their meanings by connecting to real-world sensorimotor experiences. Recent work has shown preliminary evidence that grounding may emerge in (vision-)language…
This paper continues the study of K-theoretic invariants for semigroup C*-algebras attached to ax+b-semigroups over rings of algebraic integers in number fields. We show that from the semigroup C*-algebra together with its canonical…
Moving from the mathematical theory of (abstract) syntax, we develop a general relational theory of symbolic manipulation parametric with respect to, and accounting for, general notions of syntax. We model syntax relying on categorical…
In this paper, we construct a new homology theory for semi-groups satisfying the self distributivity axiom or the idempotency axiom. Next, we consider the geometric realization corresponding to the homology theory. We continue with the…
This perspective paper explores the bidirectional influence between language emergence and the relational structure of subjective experiences, termed qualia structure, and lays out a constructive approach to the intricate dependency between…