Categorical abstract algebraic logic weakly referential π-institutions Cover Image

Categorical abstract algebraic logic weakly referential π-institutions
Categorical abstract algebraic logic weakly referential π-institutions

Author(s): George Voutsadakis
Subject(s): Philosophy, Logic
Published by: Wydawnictwo Uniwersytetu Jagiellońskiego

Summary/Abstract: Wojcicki 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 Wojcicki asserts that a logic has a referential semantics if and only if it is selfextensional. A second theorem of Wojcicki 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 -institution has a weakly referential semantics if and only if it is weakly self-extensional.

  • Issue Year: 2016
  • Issue No: 51
  • Page Range: 91-103
  • Page Count: 13
  • Language: English