Sesión Lógica y ComputabilidadA categorial equivalence for tense semi-implicative lattice
María Isabel Pelegrina
Universidad Nacional de San Juan, Instituto de Ciencias Básicas, Facultad de Filosofía Humanidades y Artes, Argentina - Esta dirección de correo electrónico está siendo protegida contra los robots de spam. Necesita tener JavaScript habilitado para poder verlo.
Implicative semilattices are the algebraic models of the implication conjunction fragment of Intuitionistic Propositional Logic [1]. In [4], Liang and Lin study tense operators $G$, $H$, $F$, and $P$ on implicative semilattices and define the variety of tense implicative semilattices, denoted by ${tIS}$. These structures serve as the algebraic models of the disjunction-free fragment of Ewald’s intuitionistic tense logic [2, 3].
In this paper, we introduce the varieties of tense bounded implicative semilattices, denoted by ${tIS_0}$ and of tense bounded implicative semilattices which satisfy the additional condition G(0) = 0 = H(0), denoted by ${tIS_0^+}$ and investigate some of their fundamental properties. We then extend Kalman's functor to this tense setting, establishing a categorical equivalence between the variety ${tIS_0^+}$ and a subcategory of centered tense $KIS_0$-algebras. Finally, we analyze tense congruences in these algebras, introduce a class of well-behaved congruences, and characterize them via tense filters, thus providing a lattice-theoretic perspective on the congruence structure of ${ tIS_0^+}$-algebras.
Trabajo en conjunto con: Gustavo Pelaitay (CONICET and Universidad Nacional de San Juan, Instituto de Ciencias Básicas, Facultad de Filosofía Humanidades y Artes, Argentina) y Maria Isabel Galoviche (Universidad Nacional de San Juan, Instituto de Ciencias Básicas, Facultad de Filosofía Humanidades y Artes, Argentina).
Referencias
[1] Curry, H. B. Foundations of Mathematical Logic. McGraw-Hill, 1963.
[2] Ewald, W. B. Intuitionistic tense and modal logic. The Journal of Symbolic Logic, 51 (1), 166 - 179, 1986.
[3] Figallo, A. V. and Pelaitay, G. An algebraic axiomatization of the Ewald’s intuitionistic tense logic. Soft Computing, 18 (10), 1873 - 1883, 2014.
[4] Liang, F. and Lin, Z. On the Decidability of Intuitionistic Tense Logic without Disjunction. Proc. 29th Int. Joint Conf. on Artificial Intelligence (IJCAI-20), 1805 - 1811 (2020).