Propositional logic •Basic elements are propositional variables e.g., P 1,1 (refer to facts about the world) •Possible worlds: mappings from variables to T/F First-order logic •Basic elements are terms, e.g., George, banana-of(George), binders-full-of(banana-of(George)) (logical expressions that refer to objects) First Order Logic - Satisﬁability and Validity ... Is there some interpretation I, such that I |= F? First-order logic is also called Predicate logic and First-order predicate calculus (FOPL). First-Order Logic (Predicate Calculus) Summary of Deﬁnitions and Main Results CS 245 1 Syntax of First-Order Logic Deﬁnition 1 (Alphabet of First-Order Terms and Formulæ) ... Let Ibe an interpretation, a valuation, ta term, xa variable. First-order logic is a powerful language that develops information about the objects in a more easy way and can also express the relationship between those objects. ... rules to conclude validity in the Socrates example. Otherwise, a deductive argument is said to be invalid. is the predicate true of these arguments. Introduction Part 1: First-Order Logic • formalizes fundamental mathematical concepts • expressive (Turing-complete) • not too expressive (not axiomatizable: natural numbers, uncountable sets) • rich structure of decidable fragments • rich model and proof theory First-order logic is also called (ﬁrst-order) predicate logic. Symbolic Logic Notes on the Interpretation of First-Order Logic Notes for Symbolic Logic Fall 2005 John N. Martin , one cannot have variables that stand for books or tables. Satisﬁability and Validity The Inference Rule Method The Semantic Argument Method Inference in First-Order Logic is used to deduce new facts or sentences from existing sentences. Substitution: Substitution is a fundamental operation performed on … First-order logic, also known as quantification theory and predicate calculus is a term that refers to predicate logics in which quantified predicates may range over a single domain of discourse that contains distinct objects. Owns(John,Car1) Sold(John,Car1,Fred) Semantics is True or False depending on the interpretation, i.e. First Order Logic (4A) Implication 9 Young Won Lim 5/30/17 PL: Validity of Arguments (2) A deductive argument is said to be valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false. A ﬁrst-order predicate logic sentence G is satisﬁable if, and only if, :G is not a tautology. It is a formal representation of logic in the form of quantifiers. for the premises to be true and the conclusion is false. Before understanding the FOL inference rule, let's understand some basic terminologies used in FOL. “It is raining”. 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