An interpretation is an assignment of meaning to the symbols of a formal language. Many formal languages used in mathematics, logic, and theoretical computer science are defined in solely syntactic terms, … 展开

The formal language for propositional logic consists of formulas built up from propositional symbols (also called sentential symbols, … 展开

A formal language for higher-order predicate logic looks much the same as a formal language for first-order logic. The difference is that there are now many different types of variables. Some variables correspond to elements of the domain, as in first-order … 展开

A formal language consists of a possibly infinite set of sentences (variously called words or formulas) built from a fixed set of letters or symbols. The inventory from which these letters are … 展开

Many of the commonly studied interpretations associate each sentence in a formal language with a single truth value, either True or … 展开

Unlike propositional logic, where every language is the same apart from a choice of a different set of propositional variables, there are many different first-order languages. Each first-order language is defined by a signature. The signature consists of a set of non … 展开

The interpretations of propositional logic and predicate logic described above are not the only possible interpretations. In particular, there are other types of interpretations that are used in the study of non-classical logic (such as intuitionistic logic), … 展开