Quantifier-Free Equational Logic and Prime Implicate Generation

2015 ◽  
pp. 311-325 ◽  
Author(s):  
Mnacho Echenim ◽  
Nicolas Peltier ◽  
Sophie Tourret
Keyword(s):  
Equational Logic

Remarks on remarks on many-sorted equational logic

1987 ◽  
Vol 22 (4) ◽  
pp. 41-48 ◽  
Author(s):  
J A Goguen ◽  
J Meseguer
Keyword(s):  
Equational Logic

Interpolation in Conditional Equational Logic1

1991 ◽  
Vol 15 (1) ◽  
pp. 80-85
Author(s):  
P.H. Rodenburg
Keyword(s):  
Interpolation Theorem ◽  
Equational Logic ◽  
Craig’S Interpolation Theorem ◽  
Natural Formulation

In a natural formulation, Craig’s interpolation theorem is shown to hold for conditional equational logic.

Completeness of many-sorted equational logic

1982 ◽  
Vol 17 (1) ◽  
pp. 9-17 ◽  
Author(s):  
J. A. Goguen ◽  
J. Meseguer
Keyword(s):  
Equational Logic

Walter Taylor. Appendix 4. Equational logic. Therein, pp. 378–400.

1982 ◽  
Vol 47 (2) ◽  
pp. 451-451
Author(s):  
Heinrich Werner
Keyword(s):  
Equational Logic

Fuzzy equational logic

2002 ◽  
Vol 41 (1) ◽  
pp. 83-90 ◽  
Author(s):  
Radim Bělohlávek
Keyword(s):  
Equational Logic

scholarly journals Power Matrices and Dunn--Belnap Semantics: Reflections on a Remark of Graham Priest

2014 ◽  
Vol 11 (1) ◽  
Author(s):  
Lloyd Humberstone
Keyword(s):  
Equational Logic ◽  
Consequence Relations ◽  
Consequence Relation ◽  
Power Matrix ◽  
Matrix Construction ◽  
The Given ◽  
The Universe ◽  
Power Algebras ◽  
Graham Priest ◽  
Natural Way

The plurivalent logics considered in Graham Priest's recent paper of that name can be thought of as logics determined by matrices (in the `logical matrix' sense) whose underlying algebras are power algebras (a.k.a. complex algebras, or `globals'), where the power algebra of a given algebra has as elements \textit{subsets} of the universe of the given algebra, and the power matrix of a given matrix has has the power algebra of the latter's algebra as its underlying algebra, with its designated elements being selected in a natural way on the basis of those of the given matrix. The present discussion stresses the continuity of Priest's work on the question of which matrices determine consequence relations (for propositional logics) which remain unaffected on passage to the consequence relation determined by the power matrix of the given matrix with the corresponding (long-settled) question in equational logic as to which identities holding in an algebra continue to hold in its power algebra. Both questions are sensitive to a decision as to whether or not to include the empty set as an element of the power algebra, and our main focus will be on the contrast, when it is included, between the power matrix semantics (derived from the two-element Boolean matrix) and the four-valued Dunn--Belnap semantics for first-degree entailment a la Anderson and Belnap) in terms of sets of classical values (subsets of {T, F}, that is), in which the empty set figures in a somewhat different way, as Priest had remarked his 1984 study, `Hyper-contradictions', in which what we are calling the power matrix construction first appeared.

Equational Logic Programming

1998 ◽  
Author(s):  
Michael J. O’Donnell
Keyword(s):  
Normal Form ◽  
Logic Programming ◽  
Programming Languages ◽  
Question Answering ◽  
Normal Forms ◽  
Equational Logic ◽  
Consequence Relation ◽  
Logic Programming Languages ◽  
Semantic Consequence

Sections 2.3.4 and 2.3.5 of the chapter ‘Introduction: Logic and Logic Programming Languages’ are crucial prerequisites to this chapter. I summarize their relevance below, but do not repeat their content. Logic programming languages in general are those that compute by deriving semantic consequences of given formulae in order to answer questions. In equational logic programming languages, the formulae are all equations expressing postulated properties of certain functions, and the questions ask for equivalent normal forms for given terms. Section 2.3.4 of the ‘Introduction . . .’ chapter gives definitions of the models of equational logic, the semantic consequence relation . . . T |=≐(t1 ≐ t2) . . . (t1 ≐ t2 is a semantic consequence of the set T of equations, see Definition 2.3.14), and the question answering relation . . . (norm t1,…,ti : t) ?- ≐ (t ≐ s) . . . (t ≐ s asserts the equality of t to the normal form s, which contains no instances of t1, . . . , ti, see Definition 2.3.16).

Sign in / Sign up

Export Citation Format

Share Document