'Conjunctive normal form' presentation slideshows

Propositional Approaches to First-Order Theorem Proving

Propositional Approaches to First-Order Theorem Proving. David A. Plaisted UNC Chapel Hill May 2004. History of AI. Early emphasis on general methods Newell Shaw Simon GPS Robinson 1965 resolution Cordell Green question answering Shift to specialized techniques Feigenbaum Expert Systems

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Logical Agents

Logical Agents. Knowledge bases. Knowledge base = set of sentences in a formal language Declarative approach to building an agent (or other system): Tell it what it needs to know Then it can Ask itself what to do answers should follow from the KB

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Warm-up

Warm-up. The regions below visually enclose the set of models that satisfy the respective sentence or . For which of the following diagrams does entail . Select all that apply. A). B). C). D). E). Warm-up. : iff in every world where is true, is also true.

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Problem Spaces P/NP

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Intelligent Systems (AI-2) Computer Science cpsc422 , Lecture 20 Mar, 3, 2014

Intelligent Systems (AI-2) Computer Science cpsc422 , Lecture 20 Mar, 3, 2014. Slide credit: some slides adapted from Stuart Russell (Berkeley ), some from Padhraic Smyth ( UCIrvine ). 422 big picture. Hybrid. Prob relational models Prob CFG Markov Networks. Deterministic.

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Propositional Equivalences

Propositional Equivalences. Section 1.3. More Logical Equivalences. Constructing New Logical Equivalences. We can show that two expressions are logically equivalent by developing a series of logically equivalent statements.

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The Satisfiability Problem

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10.3 - Restricted Satisfiability (SAT) Problem

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Time Complexity

Time Complexity. Consider a deterministic Turing Machine which decides a language . For any string the computation of terminates in a finite amount of transitions. Initial state. Accept or Reject. Decision Time = #transitions. Initial state. Accept or Reject.

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NP-Completeness

NP-Completeness. Lecture for CS 302. Traveling Salesperson Problem. You have to visit n cities You want to make the shortest trip How could you do this? What if you had a machine that could guess?. Non-deterministic polynomial time.

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NP-Completeness

NP-Completeness. Lecture for CS 302. Traveling Salesperson Problem. You have to visit n cities You want to make the shortest trip How could you do this? What if you had a machine that could guess?. Non-deterministic polynomial time.

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Prepositional Logic

Prepositional Logic. Lecture 5. Logical Equivalence. A stronger form of implication is expressed by the statement B is TRUE if and only if A is TRUE. This is usually written as A ?? B and is called logical equivalence The double arrow signifies that A ?? B is the same as A?B AND B?A

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Chapter 8 Inference and Resolution for Problem Solving

Chapter 8 Inference and Resolution for Problem Solving. Chapter 8 Contents (1). Normal Forms Converting to CNF Clauses The Resolution Rule Resolution Refutation Proof by Refutation Example: Graph Coloring. Chapter 8 Contents (2). Normal Forms in Predicate Calculus Skolemization

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Logical Agents

Logical Agents. (Chapter 7 of Russell & Norvig). Outline. Knowledge bases Logic Propositional (Boolean) Logic Normal forms Inference Rules. Knowledge bases. knowledge base = set of sentences in a formal language Declarative approach to building KB Query approach to extracting knowledge.

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Propositional and First Order Reasoning

Propositional and First Order Reasoning. Terminology. Propositional variable: boolean variable (p) Literal: propositional variable or its negation p ?p Clause: disjunction of literals q / ? p / ? r given by set of literalsL {q, ? p, ? r}

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Review of Propositional Logic Syntax

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Fitting a Function to the Difficulty of Boolean Formulas

Fitting a Function to the Difficulty of Boolean Formulas. Greg Dennis NMM Final Project. Motivation. Difficulty of boolean formulas varies greatly difficulty = # decisions by solver = time to solve difficulty varies between formulas of same size Difficulty depends on many factors

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Knowledge Representation & Reasoning

Knowledge Representation & Reasoning. Lecture 6: Logic Programming in First Order Logic (FOL). By : SHEREENA ARIF Room : T2//8, BLOK 4 Email : shereen@ftsm.ukm.my OR shereen.ma@gmail.com. Conversion to CNF. Conjunctive Normal Form : a conjunction of clauses

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Boolean Satisfiability Present and Future

Boolean Satisfiability Present and Future. Lintao Zhang Microsoft Research SVC. SAT: Introduction . Deciding the satisfiability of Boolean formulas SAT: Propositional ( usually in Conjunctive Normal Form (CNF) ) QBF: With quantifiers Many driving forces Verification

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