Информационная система "Конференции"

Abstracts

Applications of logic in computer science

Archetypal dynamics is a formal approach to the study of emergence in complex systems. It is based upon a study of meaning laden information flows in complex systems. Its central primitive notion is that of a semantic frame, which formalizes the notion of a frame of reference through means of which one interacts with the system at hand. As in logic where one has notions of model and theory, here one has notions of realisation (system) and interpretation (user/agent). Archetypal dynamics postulates that emergence occurs whenever a complex system is capable of realising multiple independent semantic frames. The main formal structure for representing this situation is the tapestry.

{bf Definition:} A {em tapestry} is a 4-tuple $(L,S,R,lOmega)$ where

begin{enumerate}

item $I$ is a collection of {em informons}

item $S$ is a collection of {em struts}

item $R$ is a collection of {em relators}

item $Omega$ is a collection of meaning labels with assignment map $l:Scup Rrightarrow Omega$

item $T_{S}=(I,S,Omega)$ is an $Omega$-labelled, directed graph

item $T_{R}=(I,R,Omega)$ is an $Omega$-labelled, directed multigraph

item Given any $a,bin I$ and label $alpha$, there exist at most two $alpha$-labelled relators, $r,r'in R$ with $r:astackrel{alpha}{rightarrow}b$ and/or $r':bstackrel{alpha}{rightarrow}a$.

item For any $a,bin I$ and any $alpha$-labelled relator $rin R$ with $r:astackrel{alpha}{rightarrow}b$, there exists exactly one $nin I$ and $alpha$-labelled struts $s,s'in S$ such that $s:nstackrel{alpha}{rightarrow}a$ and $s':nstackrel{alpha}{rightarrow}b$.

item Every $nin I$ is either a vertex of some $rin R$ or an initial vertex of some $sin S$, or both. That is, there are no isolated vertices.

end{enumerate}

Elements of $I$, serve either as elements of relations (loci) or as markers of relations (nexi) depending upon the absence or presence of struts. The tapestry provides a representation of information events (informons) and of meaning laden coherences linking these events. These linkages may be public, private, active, or passive, depending upon the meanings associated with the label set $Omega$ and so reflect the many varied attributes attached to information in a computer science setting.

Realisations are represented through general tapestries (akin to model), while interpretations are represented through formal tapestries (akin to theory). Tapestries themselves are created through a process of weaving using constructor tapestries.

The current focus of research is to formalize ideas related to notions of semantic coherence and semantic consistency, of entity, and to apply these to the study of vertical and horizontal emergence. At present, the approach to semantic coherence and consistency is through a study of variants on the Ehrenfeucht-Fraisse Game applied to general and formal tapestries.

The process of weaving a tapestry is defined via several different combinatorial games of the type described by Conway.

Tapestries appear capable of expressing several different logics, including classical logics of multiples orders and modal logic, and there appear to be interesting connections to relation algebras and perhaps to situation theory.

In this talk, emphasis will be placed on describing the formalization of the notions of semantic coherence and consistency, and if time permits some links to classical, modal and temporal logics will be described.

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