Knowledge Representation Logic u Concepts Semantic Nets

Knowledge Representation & Logic u. Concepts: Semantic Nets & propositional logic u Readings: Semantic Nets (Winston chap. 2) u Readings: Russell & Norvig (Chap 6) B. M. Ombuki COSC 3 P 71 1

Knowledge representation? We will discuss knowledge representation from two aspects: - knowledge representation and semantic nets - knowledge representation that is concerned with the syntax and semantics of the language of propositional logic B. M. Ombuki COSC 3 P 71 2

Knowledge Representation • Core problem in developing an intelligent system: knowledge representation: express knowledge in a computer-tractable form • Knowledge representation: a description that incorporates information about a problem, environment, entity, . . . • Primary focus of knowledge representation is two fold; - How to represent the knowledge one has about a problem domain - How to reason using that knowledge in order to answer questions or make decisions • Knowledge representation deals with the problem of how to model the world sufficiently for intelligent action • Knowledge-based agents know something about their environment and they use their knowledge together with an inference engine to reason about their environment. B. M. Ombuki COSC 3 P 71 3

How essential is KR ? • A ‘problem’ involves relationships between concrete objects, abstract concepts • relationship: dependencies, constraints, independencies, . . . – an appropriate KR makes these explicit, and clarifies them so as to model them succinctly and without unnecessary details – once the KR is designed, then the essence of the problem is clear – good representation is key to good problem solving – once an appropriate KR is arrived at for a given problem, the problem is almost solved B. M. Ombuki COSC 3 P 71 4

KR • If we didn’t have a useful KR, the problem solving algorithm would have to incorporate the problem details within itself – result (at best): unwieldy, complex algorithm – worse result (probably): cannot solve problem, because the problem definition is unclear and abstruse B. M. Ombuki COSC 3 P 71 5

Evaluating KR • How do you know that a particular KR is good? – Explicitness: clarity is important in expressing state of problem at a glance – constraints: expressing how objects, relations influence each other – suppress irrelevant detail – transparency: easy to understand – completeness: all problem variations can be handled – concise: compact and clear – fast: quick access for reads, writes, updates – computable: their creation can be automated • A problem can be represented in more than one way – which is preferrable depends on the goals for the problem solving task and above goals B. M. Ombuki COSC 3 P 71 6

Semantic Nets and Knowledge Representation • A representation can be viewed as having four components: 1. Lexical: what symbols are used (vocabulary or lexicon) • labels for objects, links • e. g. . chess pieces, board positions, board move links • e. g. . duck, farmer, moose, boat trip links 2. structural: constraints describing how symbols can be arranged • structure of KR: how are nodes and links connected? 3. semantic: the meaning or interpretation of the lexical and structural components • what are they denoting wrt the problem at hand? 4. procedural: the means to use the KR to solve a problem • may be many; likely there is one that uses that particular KR to best advantage B. M. Ombuki COSC 3 P 71 7

Semantic Nets • semantic net: a representation in which nodes represent objects, links displays relations between objects, and link labels denote the particular relations • syntactically, semantic nets are labeled graphs – more than merely a data structure: the representations that nodes and links denote are important --> the semantics • due to their generality, semantic nets are the foundation of many KR schemes – they are often specialized according to the application B. M. Ombuki COSC 3 P 71 8

Semantic Nets A farmer, fox, goose and grain needs to move across a river in a boat. Constraint: boat can only carry the farmer and one other occupant at a time. Condition: Fox should not be left unattended with goose and goose should not be left with grains. What should the farmer do? Figure 2. 1: (Winston P 17) Problem of Farmer B. M. Ombuki COSC 3 P 71 9

Semantic nets • • • lexical: nodes, link labels structural: nodes interconnected with labeled links semantics: depends on application procedural: include procedures to read, write, update the net eg. Farmer problem in text – lexical: • nodes: represent configurations of farmer, goose, fox, grain, and river bank orientation • links: canoe trips • link labels: not too critical here (“canoe trip”), arrows important – structural: the connections that do not result in an eaten entity – semantic: we ascribe the semantic net our “intended interpretation” wrt the problem as a whole B. M. Ombuki COSC 3 P 71 10

Example Lintel GO 258 g 0034 G 088 g 0075 is-supported by G 083 left post is-supported by Right post Equivalence semantics: relates description in the representation to descriptions in other representations with meaning Procedural semantics: set of programs (defined) operates on descriptions in representation Descriptive semantics: explanations of what descriptions mean in a language we understand (e. g above example) Note: equivalence semantics & procedural semantics Descriptive semantics B. M. Ombuki COSC 3 P 71 11

Semantic nets • note the similarity between KR / semantic nets in AI problem solving, and data structures and computer programs – especially how an appropriate net / data structure simplifies problem solving / program • note that we can find mappings between representations – hence there is no “most powerful” net – but one net might be clearer than another • Homework: Read on taxonomy of nets described in Winston (p. 21, fig 2. 2) B. M. Ombuki COSC 3 P 71 12

Using semantics nets We will look at a few examples of the use of Semantic nets 1. matching Describe and match method: (i) describe object using a suitable representation (i. e. in the ‘language’ you understand) (ii) look it up in your library of known objects for a match or until no more library descriptions found (iii) announce success if found, or failure. fig 2. 4 Winston (p. 23) see next slide B. M. Ombuki COSC 3 P 71 13

Example: Matching object Description Library identify object by describing it identify B. M. Ombuki COSC 3 P 71 Rejects 14

Illustration of describe Matching and Match • Feature-based object identifier has: (1) feature extractor: describe main characteristics of object to be identified (eg. shape, size, colour, . . . ) – these characteristics are used to construct a semantic net representation for this object – becomes a feature point - an abstract ‘coordinate’ in a multi-dimensional feature space (2) feature evaluator measures feature point distance from known objects in feature space B. M. Ombuki COSC 3 P 71 15

Example 4 3 No. of holes 2 unknown 1 8 Fig 2. 5: Winston p. 24 Area B. M. Ombuki COSC 3 P 71 16 16

1. feature-based identification in analogy problems • geometric analogy net: – nodes: geometric primitives (dots, circles, squares, . . . ) – links: (i) relations between primitives (above, inside, left of, . . . ) (ii) transformations: addition, deletion, expansion, contraction, rotation, reflection, and combinations of these • We then use this net representation to denote analogies: how one picture is related to another See Fig 2. 6 p. 25 Winston B. M. Ombuki COSC 3 P 71 17

Analogy problems Fig 2. 7 B. M. Ombuki COSC 3 P 71 18

Feature ID and analogy problems • in this rule, the transformation links are the key: when doing an analogy problem, we want to find an instance which duplicates these transformations (may be more than 1 transformation!) • the problem solver can create these transformations and relations automatically, using tricks from computer graphics (see figs 2. 8, 2. 9) • then, once we ascribe rules for all the transformations, we find the one that matches the problem specification the best – note that there many be more than one transformation per analogy – we may need to choose the best of many: need a way to judge B. M. Ombuki COSC 3 P 71 19