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Categorical abstract algebraic logic weakly referential π-institutions

Voutsadakis G.

Reports on Mathematical Logic

2016

Vol. 51

91--103

Wójcicki introduced in the late 1970s the concept of a referential semantics for propositional logics. Referential semantics incorporate features of the Kripke possible world semantics for modal logics into the realm of algebraic and matrix semantics of arbitrary sentential logics. A well-known theorem of Wójcicki asserts that a logic has a referential semantics if and only if it is selfextensional. A second theorem of Wójcicki asserts that a logic has a weakly referential semantics if and only if it is weakly self- extensional. We formulate and prove an analog of this theorem in the categorical setting. We show that a π-institution has a weakly referential semantics if and only if it is weakly self-extensional.