Unital Abstract Logics
Alex Citkin, Alexei Yu. Muravitsky · 2022
Abstract This chapter introduces the concept of unital abstract logic. We illustrate this concept with a number of well-known examples of logical consequence, as well as some classes of logical consequence, such as implicative logics and Fregean logics. The quintessence of this chapter is the concept of a Lindenbaum-Tarski algebra. Also in this chapter, we are developing a technique that allows us to consider the Lindenbaum-Tarski algebra as a separating tool, or at least as a starting point for creating such a means. As illustrative examples, we give a detailed description of the Lindenbaum-Tarski algebras with one and two variables of the classical propositional calculus and the Lindenbaum-Tarski algebra with one variable of the intuitionistic propositional calculus, the so-called Rieger-Nishimura algebra. We also include some applications of Lindenbaum-Tarski algebras.