First Order Logic-Predicate Logic-Artificial Intelligence-Logical Reasoning-Unit-2-15A05606

Unit - 2 - Logical Reasoning - First Order Logic / Predicate Logic
Drawbacks of Propositional Logic
Propositional logic is very simple and declarative, in which knowledge and inference are separate, and inference is entirely domain independent
Propositional logic has lack of data structure in programming.
Propositional logic is not sufficient for complex or natural language sentences.
E.g. Some students in KEC are intelligent
Propositional logic has very limited expressive power
E.g., cannot say "pits cause breezes in adjacent squares“ except by writing one sentence for each square
First Order Logic (FOL)
First-order logic is also known as Predicate logic or First-order predicate logic.
First-order logic, like natural language has well defined syntax and semantics.
It assumes the world contains
Objects: people, houses, numbers, colors, baseball games, wars, …
Relations: red, round, prime, brother of, bigger than, part of, comes between, …
Functions: father of, best friend, one more than, plus,
Properties of FOL
It has ability to represent facts about some or all of the objects and relations in the universe
Represent law and rules extracted from real world
Useful language for Mathematic , Philosophy and AI
Represent facts in realistic manner rather than just true / false
Makes ontological commitment
Syntax of FOL: Basic Elements
Constants King John, 2, NUS,...
Predicates Brother,
Functions Sqrt, Left Leg Of,
Variables x, y, a, b,...
Connectives , , , , 
Equality =
Quantifiers , 
Sentences Atom / complex sentences
Atom True / False / AP (atomic proposition)
Complex sentence (sentence) / connective sentence /
 sentence
Atomic sentences
Atomic sentence = predicate (term1,...,term) or term1 = term2
Term = function (term1,...,term) or constant or variable
Example.
Brother(King John, Richard The Lionheart)
(Length(Left Leg Of (Richard)), Length(Left Leg Of(King John)))
Complex sentences
Complex sentences are made from atomic sentences using five logical connectives
S1 and S2 are two atomic statements then
S1, S1  S2, S1  S2, S1  S2, S1  S2,
E.g. Sibling(King John, Richard)  Sibling(Richard, King John)
(1,2)  (1,2)
(1,2)   (1,2)
Truth in FOL
Sentences are true with respect to a model and an interpretation
Model contains objects (domain elements) and relations among them
Interpretation specifies referents for
Constant Symbols → Objects
Predicate Symbols → Relations
Function Symbols → Functional relations
An atomic sentence predicate(term1,...,term) is true
if the objects referred by term1,...,term
are in the relation referred by predicate
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