Download - Effective Propositional Logic Search
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Effective Propositional Logic Search
• Use WalkSAT– Use min-Conflict heuristic– Similar to hill climbing and simulated annealing– Pick unsatisfied clause then pick a symbol to flip to
satisfy the clause by• Use Min Conflict• Or Random
• Downside will fins solution if they exists fast but not good if no solution exits as it keeps running but faster than David Putman search
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First order Logic
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First Order Logic(AKA-Predicate Calculus) vs (Propositional Logic)
• Propositional Logic we talk about atomic facts– Propositional logic has no objects. – Because it has no objects it also has no relationships
between objects, or functions that names objects • FOL- Stronger ontological commitment– Objects (with individual identities)– Objects have properties– Relations between objects
• FOL is very well understood
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First Order Logic Syntax
ForAll | ThereExists
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First order logic has• SENTENCES that represent Boolean facts• TERMS which represent objects
• CONSTANTS and VARIABLES which represent objects• PREDICATE which given an object (I.e. TERM) it
returns true or false• FUNCTIONS which given an object will return
another object
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• All students are WPI are smart.
• There exists a student at WPI that is smart
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• All students are WPI are smart.– AtWPI(x) means a person is at WPI– Smart(y) means person y is smart.– ForAll(x) AtWPI(x)=> Smart(x)
• There exists a student at WPI that is smart• ThereExists(x) AtMIT(x) ^ Smart(x)
• What does this mean?• s at(s,MIT) => smart(s)– If there is an object that is not at MIT then this statement will be
true
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Equality :Define Sibling
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ForAll x,y Sibling(x,y) not(x=y) AND [ThereExists p Parent(p,x)
AND Parent(p,y)]
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FOL
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UnificationA substitution x unifies an atomic sentence p and q if px=qx
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UnificationA substitution x unifies an atomic sentence p and q if px=qx
Mother(John)}
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Industrial Strength Inference
• Completeness• Resolution• Logic Programming
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Horn Clauses• A Horn Clause is a disjuntion of literals with the additional
caveat that there is at most one positive literal.• ~a v b v ~c is a Horn Clause (a ^ c) => b • ~a v ~b v ~c is very Horn (a ^ b ^ c) => True• ~a v b v c is not a Horn Clause(a => b v c) • All Horn Clause can we written as a implication where there
are a set of things anded together to imply a literal• A V B => C • Easy to understand.• Entailment can be decided in linear time in the size of the KB
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Completeness in FOL?
• Forward and backward chaining are complete for Horn Clause Knowledge Bases but incomplete for general first order logic
• Eg
• But should be able to infer Rich(Me) but FC/BC won’t do it
• Does a complete algorhtm exist?
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Draw a proof
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