What is the case (a fact) is the existence of states of affairs. A logical picture of facts is a thought. A thought is a proposition with a sense. A proposition is a truth-function of elementary propositions. (An …

Decidability of FOL FOL is undecidable (Turing & Church) 2- 21 There does not exist an algorithm for deciding if a FOL formula F is valid, i.e. always halt and says “yes” if F is valid or say “no” if F is …

Gödel's Incompleteness Theorem Completeness Theorem: All valid statements have proofs in FOL Incompleteness Theorem: For any FOL KB enhanced to allow mathematical induction, there are true …

By adding to the formalism of FOL the notion of sort, we can obtain a flexible and convenient logic called many-sorted first-order logic, which has the same properties as FOL.

While formulas in PL evaluate to true or false, terms in FOL evaluate to values in an underlying domain such as integers, strings, lists, etc. Terms in FOL are defined by the grammar:

Definition of first-order logic: syntax and semantics What is FOL good for? Note good section 8.1 in AIMA4e: talks about relationships among di erent logics, including probability theory and fuzzy logic. …

First-order logic Now let’s get. down to business! This chapter starts with an overview of classical first-order logic (FOL) – meaning standard propositional and predicate logic – which is at the core of any …