Predicate Logic with Definitions

Abstract

Predicate Logic with Definitions (PLD or D-logic) is a modification of first-order logic intended mostly for practical formalization of mathematics. The main syntactic constructs of D-logic are terms, formulas and definitions. A definition is a definition of variables, a definition of constants, or a composite definition (D-logic has also abbreviation definitions called abbreviations). Definitions can be used inside terms and formulas. This possibility alleviates introducing new quantifier-like names. Composite definitions allow constructing new definitions from existing ones.