Algebraic Semantics for Graded Propositions.
Haythem O. Ismail, Nourhan Ehab · 2015
We present LogAG, an algebraic language for reasoning about graded propositions. LogAG is algebraic in that it is a language of only terms, some of which denote propositions. Both propositions and their grades are taken as individuals in the LogAG ontology. Thus, the language includes terms denoting graded propositions, grades of propositions, grading propositions, and graded grading propositions in an arbitrary compositional structure. In this paper, we present the syntax and semantics of LogAG, defining an infinite sequence of graded logical consequence relations, each corresponding to accepting graded propositions at some nesting depth. We show the utility of LogAG in default reasoning, reasoning about information provided by a chain of sources with varying degrees of trust, and representing the dilemma one is in when facing paradoxical liar-like sentences.