Knowledge Representation & Logic Concepts: Semantic Nets & propositional logic Readings: Semantic Nets (Winston chap. 2) Readings: Russell & Norvig (Chap 6) B.M.Ombuki COSC 3P71

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 3P71

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 3P71

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 3P71

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 3P71

How do you know that a particular KR is good? 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 3P71

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 3P71

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 3P71

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 P17) Problem of Farmer B.M.Ombuki COSC 3P71

Semantic nets lexical: nodes, links, 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 3P71

Example Lintel Right post left is-supported by GO258 G088 G083 g0075 g0034 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 3P71

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 3P71

Using semantics nets 1. matching Describe and match method: 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 3P71

Example:Matching Library object Description Rejects identify identify object by describing it Rejects identify B.M.Ombuki COSC 3P71

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 3P71

Example Area Fig 2.5: Winston p.24 4 3 2 unknown 1 8 No. of holes 16 B.M.Ombuki COSC 3P71

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 3P71

Analogy problems Fig 2.7 B.M.Ombuki COSC 3P71

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 3P71