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Equality Logic
- Source :
- Bulletin of the Section of Logic, Vol 49, Iss 3, Pp 291-324 (2020)
- Publication Year :
- 2020
- Publisher :
- Lodz University Press, 2020.
-
Abstract
- In this paper, we introduce and study a corresponding logic to equality-algebras and obtain some basic properties of this logic. We prove the soundness and completeness of this logic based on equality-algebras and local deduction theorem. We show that this logic is regularly algebraizable with respect to the variety of equality∆-algebras but it is not Fregean. Then we introduce the concept of (prelinear) equality∆-algebras and investigate some related properties. Also, we study ∆-deductive systems of equality∆-algebras. In particular, we prove that every prelinear equality ∆-algebra is a subdirect product of linearly ordered equality∆-algebras. Finally, we construct prelinear equality ∆ logic and prove the soundness and strong completeness of this logic respect to prelinear equality∆-algebras.
- Subjects :
- Logic
010102 general mathematics
equality logic
prelinear equality∆-algebra
many-valued logic
completness
lcsh:Logic
01 natural sciences
010101 applied mathematics
Philosophy
TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES
Computer Science::Logic in Computer Science
ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION
prelinear equality∆ logic
0101 mathematics
lcsh:BC1-199
Subjects
Details
- Language :
- English
- ISSN :
- 01380680
- Volume :
- 49
- Issue :
- 3
- Database :
- OpenAIRE
- Journal :
- Bulletin of the Section of Logic
- Accession number :
- edsair.doi.dedup.....ecce5bb54e876019e39298ecc976e845