scholarly journals A Formal Mathematical Semantics of Advanced Operations of Multiset Table Algebra

2015 ◽  
Author(s):  
Iryna Glushko
Keyword(s):  
Table Algebra ◽  
Mathematical Semantics

Outer Set Operations of Table Algebra of Infinite Tables

2016 ◽  
pp. 011-016
Author(s):  
I.N. Glushko ◽  
Keyword(s):  
Set Operations ◽  
Table Algebra ◽  
Mathematical Semantics

Table algebra of infinite tables is considered. The signature of table algebra of infinite tables is filled up with outer set operations. A formal mathematical semantics of these operations is defined.

A Two-Part Defense of Intuitionistic Mathematics

2021 ◽  
Vol 14 ◽  
pp. 26-38
Author(s):  
Samuel R. Elliott ◽  
Keyword(s):  
Alternative Interpretation ◽  
Alternative Conception ◽  
Suitable Candidate ◽  
Michael Dummett ◽  
Intuitionistic Mathematics ◽  
Mathematical Semantics

The classical interpretation of mathematical statements can be seen as comprising two separate but related aspects: a domain and a truth-schema. L. E. J. Brouwer’s intuitionistic project lays the groundwork for an alternative conception of the objects in this domain, as well as an accompanying intuitionistic truth-schema. Drawing on the work of Arend Heyting and Michael Dummett, I present two objections to classical mathematical semantics, with the aim of creating an opening for an alternative interpretation. With this accomplished, I then make the case for intuitionism as a suitable candidate to fill this void.

scholarly journals Vicious Circle Principle and Logic Programs with Aggregates

2014 ◽  
Vol 14 (4-5) ◽  
pp. 587-601 ◽  
Author(s):  
MICHAEL GELFOND ◽  
YUANLIN ZHANG
Keyword(s):  
Knowledge Representation ◽  
Vicious Circle ◽  
Logic Programs ◽  
Vicious Circle Principle ◽  
Knowledge Representation Language ◽  
Representation Language ◽  
Answer Sets ◽  
Mathematical Semantics

AbstractThe paper presents a knowledge representation language $\mathcal{A}log$ which extends ASP with aggregates. The goal is to have a language based on simple syntax and clear intuitive and mathematical semantics. We give some properties of $\mathcal{A}log$, an algorithm for computing its answer sets, and comparison with other approaches.

Abstract continuations: a mathematical semantics for handling full jumps

1988 ◽  
Author(s):  
Matthias Felleisen ◽  
Mitch Wand ◽  
Daniel Friedman ◽  
Bruce Duba
Keyword(s):  
Mathematical Semantics

TABLE ALGEBRAS OF RANK 3 AND ITS APPLICATIONS TO STRONGLY REGULAR GRAPHS

2013 ◽  
Vol 12 (05) ◽  
pp. 1250216 ◽  
Author(s):  
A. HOSSEINI ◽  
A. RAHNAMAI BARGHI
Keyword(s):  
Regular Graph ◽  
Coding Theory ◽  
Sufficient Conditions ◽  
Algebraic Approach ◽  
Strongly Regular Graph ◽  
Direct Consequence ◽  
Primitive Idempotents ◽  
Strongly Regular ◽  
Table Algebra ◽  
Integral Table Algebra

A table algebra is called quasi self-dual if there exists a permutation on the set of primitive idempotents under which any Krein parameter is equal to its corresponding structure constants. In this paper we investigate the question of when a table algebra of rank 3 is quasi self-dual. As a direct consequence we find necessary and sufficient conditions for the Bose–Mesner algebra of a given strongly regular graph to be quasi self-dual. In fact, our result generalizes the well-known Delsarte's characterization of a self-duality of the Bose–Mesner algebra of a strongly regular graph given in [P. Delsarte, An algebraic approach to the association schemes of coding theory, Philips Res. Rep. Suppl.10 (1973) 1–97]. Among our results we determine conditions under which the Krein parameters of an integral table algebra of rank 3 are non-negative rational numbers.

scholarly journals Top-down mathematical semantics and symbolic execution

1983 ◽  
Vol 17 (1) ◽  
pp. 55-70 ◽  
Author(s):  
G. Lévi ◽  
A. M. Pegna
Keyword(s):  
Symbolic Execution ◽  
Top Down ◽  
Mathematical Semantics

scholarly journals Table Algebra of Infinite Tables, Multiset Table Algebra, and their Relationship

2021 ◽  
Vol 8 ◽  
pp. 34-37
Author(s):  
Iryna Lysenko
Keyword(s):  
Table Algebra ◽  
The Relationship

The paper is focused on some theoretical questions of the table databases. Two mathematical formalisms such as table algebra of infinite tables and multiset table algebra are considered. Basic definitions referring to these formalisms are given. This paper also addresses the issue of the relationship between table algebra of infinite tables and multiset table algebra. It is proved that table algebra of infinite tables is not a subalgebra of multiset table algebra since it is not closed in relation to some signature operations of multiset table algebra. These signature operations are determined.

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