Free equivalential algebras

Mathematical Logic Qtrly

2017

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Section: Preliminariesmentioning

confidence: 99%

“…Example 3.2.2). To prove the converse inequality, we can modify the analogous proof for equivalential algebras contained in [, Theorem 5] and [, Theorem 8].…”

Section: Equivalential Algebras With Zero (Negation)mentioning

confidence: 99%

Algebraic semantics for the ‐fragment of and its properties

Mathematical Logic Qtrly

2017

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“…For proofs and for a fuller treatment of equivalential algebras, cf. [8,18,19]. Let A ∈ E. We say that a, b ∈ A are orthogonal, and write a ⊥ b, if abb = a and baa = b.…”

Section: Preliminariesmentioning

confidence: 99%

Algebraic semantics for the (↔, ¬¬)‐fragment of IPC

Mathematical Logic Qtrly

2011

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“…Supplementing these axioms by the identity x = xyy (or by the associativity law) we obtain the smallest non-trivial subvariety of E, which coincides with the class of Boolean groups and gives the algebraic semantics for equivalential fragment of classical logic. For a fuller treatment of equivalential algebras, see [22,23,13].…”

Section: Fregean Varieties and Equivalential Algebrasmentioning

confidence: 99%

Unification and projectivity in Fregean varieties

2011

Logic Journal of IGPL

In some varieties of algebras one can reduce the question of finding most general unifiers (mgus) to the problem of the existence of unifiers that fulfill the additional condition called projectivity. In this paper we study this problem for Fregean (1-regular and orderable) varieties that arise from the algebraization of fragments of intuitionistic or intermediate logics. We investigate properties of Fregean varieties, guaranteeing either for a given unifiable term or for all unifiable terms, that projective unifiers exist. We indicate the identities which fully characterize congruence permutable Fregean varieties having projective unifiers. In particular, we show that for such a variety there exists the largest subvariety that have projective unifiers.