Term satisfiability in FLew-algebras

0439176 - ÚI 2015 US eng V - Research Report
Haniková, Zuzana - Savický, Petr
Term satisfiability in FLew-algebras.
Cornell University, 2015. 24 s. arXiv.org e-Print archive, arXiv:1501.02250 [cs.LO].
R&D Projects: GA ČR GBP202/12/G061
Institutional support: RVO:67985807
Keywords : substructural logic * FLew-algebra * MV-algebra * satisfiability * computational complexity
Subject RIV: BA - General Mathematics
http://arxiv.org/abs/1501.02250

FLew-algebras form the algebraic semantics of the full Lambek calculus with exchange and weakening. We investigate two relations, called satisfiability and positive satisfiability, between FLew-terms and FLew-algebras. For each FLew-algebra, the sets of its satisfiable and positively satisfiable terms can be viewed as fragments of its existential theory; we identify and investigate the complements as fragments of its universal theory. We offer characterizations of those algebras that (positively) satisfy just those terms that are satisfiable in the two-element Boolean algebra providing its semantics to classical propositional logic. In case of positive satisfiability, these algebras are just the nontrivial weakly contractive algebras. In case of satisfiability, we give a characterization by means of another property of the algebra, the existence of a two-element congruence. Further, we argue that (positive) satisfiability problems in FLew-algebras are computationally hard. Some previous results in the area of term satisfiabilty in MV-algebras or BL-algebras, are thus brought to a common footing with, e.g., known facts on satisfiability in Heyting algebras.
Permanent Link: http://hdl.handle.net/11104/0242467