Knowledge Representation and Reasoning

Master of Science in Artificial Intelligence, 2011-2013 Knowledge Representation and Reasoning University "Politehnica" of Bucharest Department of Computer Science Fall 2011 Adina Magda Florea http://turing.cs.pub.ro/krr_11 curs.cs.pub.ro

Lecture 1 Lecture outline • Course goals • Grading • Textbooks and readings • AI well known companies • Syllabus • Why KR? • KR&R Challenges • What is KR&R? • Formal logic: why and how • Links for the young researcher

Course goals • Provide an overview of existing representational frameworks developed within AI, their key concepts and inference methods. • Acquiring skills in representing knowledge • Understanding the principles behind different knowledge representation techniques • Being able to read and understand research literature in the area of KR&R • Being able to complete a project in this research area

Grading • Course gradesMid-term exam 20% Final exam 30% Projects 30%Laboratory 20% • Requirements: min 7 lab attendances, min 50% of term activity (mid-term ex, projects, lab) • Academic Honesty PolicyIt will be considered an honor code violation to give or use someone else's code or written answers, either for the assignments or exam tests. If such a case occurs, we will take action accordingly.

Textbooks and Readings • Textbooks • Artificial Intelligence: A Modern Approach (2010) by Stuart Russell and Peter Norvig • Knowledge Representation and Reasoning by Ronald Brachman and Hector Levesque, Morgan Kaufman, 2004 • Computational Intelligence: a Logical Approach by David Poole, Alain Mackworth, and Randy Goebel, Oxford University Press, 1998 • Readings • Reading materials will be assigned to you. • You are expected to do the readings before the class

Syllabus 1.General knowledge representation issues Readings: http://plato.stanford.edu/entries/logic-ai/ 2.Logical agents – Logical knowledge representation and reasoning • First order predicate logic revisited, ATP Readings: AIMA Chapter 7 http://aima.cs.berkeley.edu/newchap07.pdf • Nonmonotonic logics and reasoning Readings: Non-monotonic Logic, Stanford Encyclopedia of Philosophy http://plato.stanford.edu/entries/logic-nonmonotonic/ Nonmonotonic Reasoning, G. Brewka, I. Niemela, M. Truszczynski http://www.informatik.uni-leipzig.de/~brewka/papers/NMchapter.pdf Nonmonotonic Reasoning With WebBased Social Networks http://www.mindswap.org/~katz/papers/socialnet-defaults.pdf

Syllabus • Modal logic, logics of knowledge and beliefs Readings: Modal logic on Wikipedia http://en.wikipedia.org/wiki/Modal_logic + to be announced • Semantic networks and description logics, reasoning services Readings: to be announced • Knowledge representation for the Semantic Web Readings: Ontology knowledge representation - from description logic to OWL Description Logics as Ontology Languages for the Semantic Web http://lat.inf.tu-dresden.de/research/papers/2005/BaSaJS60.pdf

Syllabus Midterm exam (written examination) – 1h 3. Rule based agents • Rete: Efficient unification Readings: The RETE algorithm http://www.cis.temple.edu/~ingargio/cis587/readings/rete.html • The Soar model, universal subgoaling and chunking –Readings: A gentle introduction to Soar, an architecture for human cognition http://ai.eecs.umich.edu/soar/sitemaker/docs/misc/GentleIntroduction-2006.pdf • Modern rule based systems Readings: to be announced

Syllabus 4. Probabilistic agents • Probabilistic knowledge representation and reasoning Readings: to be announced 5. Temporal reasoning • Readings: to be announced 6. Reasoning with actions • Planning • Readings: to be announced 7. Intelligence without representation and reasoning vs. Strong AI • Calls Debate Final exam

Links for the young researcher • AI-MAS Links of interest http://aimas.cs.pub.ro/links • Academic publishing http://en.wikipedia.org/wiki/Academic_publishing • Writing a Scientific Paper http://www.oup.com/us/samplechapters/0841234620/?view=usa • ISI Web of Knowledge http://isiwebofknowledge.com/ • Master Journal List http://science.thomsonreuters.com/mjl/ • Conference Proceedings Citation Index http://wokinfo.com/products_tools/multidisciplinary/webofscience/cpci/ • TED – Ideas worth spreading http://www.ted.com/

Lecture 1 Readings for Lecture 1: http://plato.stanford.edu/entries/logic-ai/ Readings for Lecture 2 AIMA Chapter 7 http://aima.cs.berkeley.edu/newchap07.pdf

1. Why KR? • We understand by "knowledge" all kinds of facts about the world. • Knowledge is necessary for intelligent behavior (human beings, robots). • In this course we consider representation of knowledge and how we can use it in making intelligent artifacts. • What is knowledge?

2. KR&R Challenges • Challenges of KR&R: • representation of commonsense knowledge • the ability of a knowledge-based system to tradeoff computational efficiency for accuracy of inferences • its ability to represent and manipulate uncertain knowledge and information.

3. What is KR? Randall Davis, Howard Shrobe, Peter Szolovits, MIT • A knowledge representation is most fundamentally a surrogate, a substitute for the thing itself, used to enable an entity to determine consequences by reasoning about the world. • It is a set of ontological commitments, i.e., an answer to the question: In what terms should I think about the world?

What is KR? • It is a fragmentary theory of intelligent reasoning, expressed in terms of three components: • the representation's fundamental conception of intelligent reasoning; • the set of inferences the representation sanctions; • the set of inferences it recommends.

What is KR? • It is a medium for pragmatically efficient computation, i.e., the computational environment in which reasoning is accomplished. • One contribution to this pragmatic efficiency is supplied by the guidance a representation provides for organizing information so as to facilitate making the recommended inferences. • It is a medium of human expression, i.e., a language in which we say things about the world.

What is KR? • If A represents B, then A stands for B and is usually more easily accessible than B. • Symbolic representations • Non-symbolic representations • Symbolic representations – set of propositions or statements that are believed by some agent.

4. What is Reasoning? • Reasoning is the use of symbolic representations of some statements in order to derive new ones. • Statements are abstract objects; their representations are concrete objects and can be easily manipulated. • Reasoning should scale well: we need efficient reasoning algorithms • http://plato.stanford.edu/entries/logical-consequence/

5. Models of KRR • Symbolic logic and ATP • Probabilistic • Temporal • Rules • Structured

6. Formal logic • Formal logic is the field of study of entailment relations, formal languages, truth conditions, semantics, and inference. • All propositions/statements are represented as formulae which have a semantics according to the logic in question. • Logical system = Formal language + semantics • Formal logics gives us a framework to discuss different kinds of reasoning.

6.1 Logical consequence (entailment) • Proof centered approach to logical consequence: the validity of a reasoning process (argument) amounts to there being a proof of the conclusions from the premises.

Logical consequence (entailment) • Model centered approach to logical consequence • Models are abstract mathematical structures that provide possible interpretations for each of the objects in a formal language. • Given a model for a language - define what it is for a sentence in that language to be true (according to that model) or not. • In any model in which the premises are true the conclusion is true too. (Tarski's definition of logical consequence from 1936.)

6.2 Model centered approach • Interpretation of a formula • Model of a formula • Entailment or logical consequence • A formula F is a logical consequence of a set of formulas P1,…Pniff F is true in all interpretations in which P1,…Pn are true. • P1,… Pn|= L F • T Formula F is a logical consequence of a set of formulas P1,…Pniff P1,…PnF is valid. • T Formula F is a logical consequence of a set of formulas P1,…Pniff P1…  Pn  ~F is inconsistent.

6.3 Proof centered approach • Theorem, deduction • Formal system • Inference rule • Premise set • Consequence of 

Proof centered approach • If then is deductible from   |S x • Theorems - the elements of Ei if • Demonstration| R x

Proof approach important notions • Th() – set of provable theorems in  • Monotonicity • Idempotence - multiple applications of the operation do not change the result • Th() – a fixed point operator which computes the closure of a set of formulas  according to the rules of inference • Th() – the least fixed point of this closure process

6.4 Properties of logical systems Important properties of logical systems: • Consistency - no theorem of the system contradicts another. • Soundness - the system's rules of proof will never allow a false inference from a true premise. If a system is sound and its axioms are true then its theorems are also guaranteed to be true. • Completeness - there are no true sentences in the system that cannot, at least in principle, be proved in the system. • Some logical systems do not have all three properties. Kurt Godel's incompleteness theorems show that no standard formal system of arithmetic can be consistent and complete.

Properties of logical systems • A logical system L is complete iff |= L  implies  |  (i.e., all valid formulas are provable) • A logical system L is sound iff  |  implies |= L  (i.e., no invalid formula is provable) • FOPL • Second order logics

7. Logic based representations 2 possible aims • to make the system function according to the logic • to specify and validate the design • Conceptualization of the world / problem • Syntax - wffs • Semantics - significance, model • Model - the domain interpretation for which a formula is true • Model - linear or structured • M |=S - " is true or satisfied in component S of the structure M" Model theory • Generate new wffs that are necessarily true, given that the old wffs are true - entailmentKB |=L Proof theory • Derive new wffs based on axioms and inference rules KB |-i

Linear model Extend PrL, PL Sentential logic of beliefs Uses beliefs atoms BA() Index PL with agents PrL, FOPL Situation calculus Adds states, actions Symbol level Modal logic Modal operators Knowledge level Structured models Description Logics Subsumption relationships Temporal logic Modal operators for time Linear time Branching time Dynamic logic Modal operators for actions Logics of knowledge and belief Modal operators B and K CTL logic Branching time and action BDI logic Adds agents, B, D, I

Higher order logic First order logic

8. Automated Reasoning

A logical puzzle Someone who lives in Dreadbury Mansion killed Aunt Agatha. Agatha, the butler, and Charles live in Dreadbury Mansion, and are the only people who live therein. A killer always hates his victim, and is never richer than his victim. Charles hates no one that Aunt Agatha hates. Agatha hates everyone except the butler. The butler hates everyone not richer than Aunt Agatha. The butler hates everyone Aunt Agatha hates. No one hates everyone. Agatha is not the butler. Who killed Aunt Agatha?

Slides 35-38 are from the slides First-Order Theorem Proving Peter Baumgartner NICTA, Logic and Computation Program, Canberra Peter.Baumgartner@nicta.com.au

Knowledge Representation and Reasoning