arXiv subjects

Tatjana Plotkin

Publications and source records attributed to Tatjana Plotkin.

4 recordsLinked to original sources

arXiv2017

Logically automorphically equivalent knowledge bases

Knowledge bases theory provide an important example of the field where applications of universal algebra and algebraic logic look very natural, and their interaction with practical problems arising in computer science might be very productive. In this paper we study the equivalence problem for knowledge bases. Our interest is to find out how the informational equivalence is related to the logical description of knowledge. Studying various equivalences of knowledge bases allows us to compare different knowledge bases. The main objective of this paper is logically automorphically equivalent knowledge bases. As we will see this notion gives us a good enough characterization of knowledge bases.

cs.LO↗

arXiv2015

Automata and automata mappings of semigroups

The paper is devoted to two types of algebraic models of automata. The usual (first type) model leads to the developed decomposition theory (Krohn-Rhodes theory). We introduce another type of automata model and study how these automata are related to cascade connections of automata of the first type. The introduced automata play a significant role in group theory and, hopefully, in the theory of formal languages.

cs.FL↗

arXiv2015

Decompositions and complexity of linear automata

The Krohn-Rhodes complexity theory for pure (without linearity) automata is well-known. This theory uses an operation of wreath product as a decomposition tool. The main goal of the paper is to introduce the notion of complexity of linear automata. This notion is ultimately related with decompositions of linear automata. The study of these decompositions is the second objective of the paper. In order to define complexity for linear automata, we have to use three operations, namely, triangular product of linear automata, wreath product of pure automata and wreath product of a linear automaton with a pure one which returns a linear automaton. We define the complexity of a linear automaton as the minimal number of operations in the decompositions of the automaton into indecomposable components (atoms). This theory relies on the following parallelism between wreath and triangular products: both of them are terminal objects in the categories of cascade connections of automata. The wreath product is the terminal object in the Krohn-Rhodes theory for pure automata, while the triangular product provides the terminal object for the cascade connections of linear automata.

math.RA↗

arXiv2015

Multi-sorted logic, models and logical geometry

Let $Θ$ be a variety of algebras, $(H, Ψ, f)$ be a model, where $H$ is an algebra from $Θ$, $Ψ$ is a set of relation symbols $φ$, $f$ is an interpretation of all $φ$ in $H$. Let $X^0$ be an infinite set of variables, $Γ$ be a collection of all finite subsets in $X^0$ (collection of sorts), $\widetildeΦ$ be the multi-sorted algebra of formulas. These data define a knowledge base $KB(H,Ψ, f)$. In the paper the notion of isomorphism of knowledge bases is considered. We give sufficient conditions which provide isomorphism of knowledge bases. We also study the problem of necessary and sufficient conditions for isomorphism of two knowledge bases.

cs.LO↗