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. Proof. 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) Such an alogithm could be used to decide satisfiable of first-order pred-icate logic sentences. But That means today's subject matter is first-order logic, which is extending propositional logic so … , one cannot have variables that stand for books or tables. 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. 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. Subramani First Order Logic. Satisfiability and Validity The Inference Rule Method The Semantic Argument Method A first-order predicate logic sentence G is satisfiable if, and only if, :G is not a tautology. Introduction to Articial Intelligence First-order Logic (Logic, Deduction, Knowledge Representation) Bernhard Beckert UNIVERSIT˜T KOBLENZ-LANDAU Winter Term 2004/2005 B. Beckert: KI für IM Œ p.1 First-order logic is also called Predicate logic and First-order predicate calculus (FOPL). It is a formal representation of logic in the form of quantifiers. Inference in First-Order Logic. “It is raining”. 5 Sentences in First-Order Logic •An atomic sentence is simply a predicate applied to a set of terms. In predicate logic, the input is taken as an entity, and the output it gives is either true or false. 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. Consequence There is no algorithm that decides whether a first-order predi-cate logic sentence is a tautology. for the premises to be true and the conclusion is false. Otherwise, a deductive argument is said to be invalid. First Order Logic - Satisfiability and Validity ... Is there some interpretation I, such that I |= F? Before understanding the FOL inference rule, let's understand some basic terminologies used in FOL. is the predicate true of these arguments. 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. First-order logic is also known as Predicate logic or First-order predicate logic. Inference in First-Order Logic is used to deduce new facts or sentences from existing sentences. There are several first order logics, but the most commonly studied is classical first-order logic, which is supposed to be an "extension" of Propositional logic. Owns(John,Car1) Sold(John,Car1,Fred) Semantics is True or False depending on the interpretation, i.e. ... rules to conclude validity in the Socrates example. 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