Decidability of relation algebras with weakened associativity

Németi, István

doi:10.1090/s0002-9939-1987-0884476-5

Cited by 13 publications

(4 citation statements)

References 7 publications

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“…In particular, there are two forms σ k+1 , γ k+1 ∈ F k+1 (X) each of which is satisfiable form below τ inside the free algebra Fr X Drs α (11). We also proved that these forms are disjoint (12).…”

Section: Free Algebras: Atoms and Zero-dimensional Elementsmentioning

confidence: 68%

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First order logic without equality on relativized semantics

Banerjee

Khaled

2018

Annals of Pure and Applied Logic

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Let α ≥ 2 be any ordinal. We consider the class Drsα of relativized diagonal free set algebras of dimension α. With same technique, we prove several important results concerning this class. Among these results, we prove that almost all free algebras of Drsα are atomless, and none of these free algebras contains zero-dimensional elements other than zero and top element. The class Drsα corresponds to first order logic, without equality symbol, with α-many variables and on relativized semantics. Hence, in this variation of first order logic, there is no finitely axiomatizable, complete and consistent theory.2010 Mathematics Subject Classification. Primary 03G15, 03B45, 03C95. Secondary 03G25, 03C05, 08B20.

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Section: Free Algebras: Atoms and Zero-dimensional Elementsmentioning

confidence: 68%

“…The definitions of all these classes can be found in [10] and [22]. The finite algebra property of these classes can be found in [10], [22], [11] and [29].…”

Section: Application In Logic and Related Developmentsmentioning

confidence: 99%

First order logic without equality on relativized semantics

Banerjee

Khaled

2018

Annals of Pure and Applied Logic

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“…We also note that the class of the weak associative relation algebras W A coincides with the class RRA {R,S} . In (Andréka, 1991), (Andréka et al, 1994), (Andréka et al, 1996), (Kramer, 1991), (Marx, 1999), (Marx et al, 1996a), (Maddux, 1982) and (Németi, 1987), it was shown that, for arbitrary H ⊆ {R, S, T }, the class RRA H enjoys any of the following properties if and only if T ∈ H: finite axiomatizability, decidability, finite algebra property, finite base property, weak and strong interpolation, Beth definability and super amalgamation property.…”

Section: Interesting Relativized Relation Algebrasmentioning

confidence: 99%

Weak Godel's incompleteness property for some decidable versions of the calculus of relations

Khaled

2015

Preprint

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Relativization is one of the central topics in the study of algebras of relations. Some relativized relation algebras behave much nicer than the original relation algebras. In this paper, we study the atomicity of the finitely generated free algebras of these nice classes of relativized relation algebras. In particular, we give an answer for the open problem, posed by I. Németi in 1985, which asks whether the finitely generated free algebras of the class of the weak associative relation algebras W A are atomic or not.

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“…The equational theory of WA is decidable (Németi 1987). Moreover, each WA is isomorphic to a subalgebra of an algebra 2 W , ∪, ∩, − W , ∅, W, • W ,˘, 1 , where W is a reflexive and symmetric binary relation on a set U, and x • W y = (x • y) ∩ W .…”

Section: A Relation Algebra (Ra)mentioning

confidence: 99%

Relation Algebras and their Application in Temporal and Spatial Reasoning

Düntsch

2005

Artif Intell Rev

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Qualitative temporal and spatial reasoning is in many cases based on binary relations such as before, after, starts, contains, contact, part of, and others derived from these by relational operators. The calculus of relation algebras is an equational formalism; it tells us which relations must exist, given several basic operations, such as Boolean operations on relations, relational composition and converse. Each equation in the calculus corresponds to a theorem, and, for a situation where there are only finitely many relations, one can construct a composition table which can serve as a look up table for the relations involved. Since the calculus handles relations, no knowledge about the concrete geometrical objects is necessary. In this sense, relational calculus is "pointless". Relation algebras were introduced into temporal reasoning by Allen (1983, Communications of the ACM 26(1), 832-843) and into spatial reasoning by Egenhofer and Sharma (1992, Fifth International Symposium on Spatial Data Handling, Charleston, SC). The calculus of relation algebras is also well suited to handle binary constraints as demonstrated e.g. by Ladkin and Maddux (1994, Journal of the ACM 41(3), 435-469). In the present paper I will give an introduction to relation algebras, and an overview of their role in qualitative temporal and spatial reasoning.

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Decidability of relation algebras with weakened associativity

Cited by 13 publications

References 7 publications

First order logic without equality on relativized semantics

First order logic without equality on relativized semantics

Weak Godel's incompleteness property for some decidable versions of the calculus of relations

Relation Algebras and their Application in Temporal and Spatial Reasoning

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