Related papers: Symbolic dynamics and semigroup theory
In "Denotational semantics for programming languages, balanced quasi-metrics and fixed points" (International Journal of Computer Mathematics 85 (2008), 623-630), J. Rodr\'{i}guez-L\'{o}pez, S. Romaguera and O. Valero introduced and studied…
We study various notions of dependency in semiring team semantics. Semiring teams are essentially database relations, where each tuple is annotated with some element from a positive semiring. We consider semiring generalizations of several…
We formulate some problems and conjectures about semigroups of rational functions under composition. The considered problems arise in different contexts, but most of them are united by a certain relationship to the concept of amenability.
Formal Semantics and Distributional Semantics are two important semantic frameworks in Natural Language Processing (NLP). Cognitive Semantics belongs to the movement of Cognitive Linguistics, which is based on contemporary cognitive…
This paper examines the relationship between gestures' function and form in design collaboration. It adopts a cognitive design research viewpoint. The analysis is restricted to gesticulations and emblems. The data analysed come from an…
Most instruments - formalisms, concepts, and metrics - for social networks analysis fail to capture their dynamics. Typical systems exhibit different scales of dynamics, ranging from the fine-grain dynamics of interactions (which recently…
Since the middle of the 20th century, a fierce battle is being fought between symbolic and distributed approaches to language and cognition. The success of deep learning models, and LLMs in particular, has been alternatively taken as…
The integration of lexical semantics and pragmatics in the analysis of the meaning of natural lan- guage has prompted changes to the global framework derived from Montague. In those works, the original lexicon, in which words were assigned…
Natural language semantics has recently sought to combine the complementary strengths of formal and distributional approaches to meaning. More specifically, proposals have been put forward to augment formal semantic machinery with…
Building on the dictionary between Kleinian groups and rational maps, we establish new connections between the theories of hyperbolic groups and certain iterated maps, regarded as dynamical systems. In order to make the exposition…
The kinematical foundations of Schwinger's algebra of selective measurements were discussed in a previous paper (arXiv:1905.12274) and, as a consequence of this, a new picture of quantum mechanics based on groupoids was proposed. In this…
This paper studies the classes of semigoups and monoids with context-free and deterministic context-free word problem. First, some examples are exhibited to clarify the relationship between these classes and their connection with the…
The concept of a $\Gamma$-semigroup has been introduced by Mridul Kanti Sen in the Int. Symp., New Delhi, 1981. It is well known that the Green's relations play an essential role in studying the structure of semigroups. In the present paper…
Message Sequence Charts & Sequence Diagrams are graphical models that represent the behavior of distributed and concurrent systems via the scheduling of discrete and local emission and reception events. We propose an Interaction Language…
We consider semigroups of transformations (partial mappings defined on a set $A$) closed under the set-theoretic intersection of mappings treated as subsets of $A\times A$. On such semigroups we define two relations: the relation of…
Modern approaches to semanic analysis if reformulated as Hilbert-space problems reveal formal structures known from quantum mechanics. Similar situation is found in distributed representations of cognitive structures developed for the…
Mathematical approaches to modeling the mind since the 1950s are reviewed. Difficulties faced by these approaches are related to the fundamental incompleteness of logic discovered by K. G\"odel. A recent mathematical advancement, dynamic…
In this article we discuss relations between algebraic and dynamical properties of non-cyclic semigroups of rational maps.
Students find their first course in Formal Languages and Automata Theory challenging. In addition to the development of formal arguments, most students struggle to understand nondeterministic computation models. In part, the struggle stems…
Following works of Furstenberg and Nevo and Zimmer we present an outline of a theory of stationary (or m-stationary) dynamical systems for a general acting group G equipped with a probability measure m. Our purpose is two-fold: First to…