Predikaattilaskenta

Predikaattilaskenta, often translated as predicate calculus or first-order logic, is a formal system in mathematical logic that extends propositional logic. It allows for the use of predicates, which are properties or relations that can be true or false of objects, and quantifiers, such as "for all" (universal quantifier) and "there exists" (existential quantifier).

In predikaattilaskenta, statements are formed using variables, constants, predicates, functions, logical connectives (like AND, OR, NOT, IMPLIES), and quantifiers. This enables the representation and reasoning about more complex statements than possible in propositional logic, which only deals with whole propositions. For example, in predikaattilaskenta, one can express "All humans are mortal" as a statement about the predicate "is human" and "is mortal" applied to a variable representing individuals.

The syntax of predikaattilaskenta defines how well-formed formulas (WFFs) are constructed. The semantics provide rules for interpreting these formulas in terms of models, which consist of a domain of objects and interpretations for predicates and functions. Key concepts include terms, atomic formulas, and the recursive definition of WFFs. Predikaattilaskenta is fundamental to many areas of computer science, mathematics, and philosophy, including automated theorem proving, database theory, and artificial intelligence.