Introduction to AI & AI Principles (Semester 1) WEEK 7 (07/08) [Barnden’s slides only] John Barnden Professor of Artificial Intelligence School of Computer Science University of Birmingham, UK

Entities vs Properties vs Relationships (review) uPartly a matter of taste and convenience whether you think of something as being a property of one or more things or a relationship between things. l X being stupid at time T: timed property of X, or a relationship between X and T. l X having 2 legs: a property of X, or a relationship between X and 2. l X and Y being friends as a relationship between X and Y, or a property of X and/or a property of Y, or a property of the group consisting of X and Y uProperties and relationships are also, in principle, entities. But usually the entities are confined to those that we want to state properties of or relationships between.

Groups of Entities: Some Examples uA group of people going out together. uThe set of prime numbers less than 100. uA couple’s children. uThe thoughts you had yesterday. uThe industrial strikes that have occurred in the UK in the last ten years. uThe set of time instants between now and a minute from now. uYour limbs.

Groups versus Entities uAny conceivable group is in principle an entity. But it may not be included in the set of entities of interest. uWhen a group is regarded as an entity, it is possible for its members to be entities in their own right as well. uIt’s largely a matter of taste/convenience whether you regard a complex object as one entity or a group of entities or both. l Extreme example: a person could be regarded as the set of molecules in his/her body. Usually it’s not convenient to do this!

Generalization/Quantification  Don't want to refer only to particular entities.Need to have representations that are about, for example, everyone in a room, without having to list them all some unidentified buildings in a city an unidentified pen in your bag a few, several or many places you have been five of the lecturers in the School and so forth.  Case of referring to every thing with particular characteristics: UNIVERSAL generalization/quantification.  Case of referring to a or some things with particular characteristics: EXISTENTIAL generalization/quantification.

Propositional Structure  Want to be able to join statements together in various ways. John is happy AND Mary is sad John is happy OR Mary is sad IF John is happy THEN Mary is sad Mary is sad BECAUSE John is happy AFTER Mary cried, John was happy and so forth.  Need to able to negate statements. It's NOT the case that John is happy.  AND (  ), OR (  ), IF-THEN (  ), negation (  ) and some closely related things are (to some extent) captured by “Propositional" (or “Sentential”) Logic … … and that's all it captures (in its basic forms).

A Taste of “Predicate Logic”  Predicate logic adds ability to deal also with entities, properties and relationships explicitly, as well as universal generalization (  ) and existential generalization (  ).  Some examples of predicate logic expressions: happy(TheodosiaKirkbride) taller-than(TheodosiaKirkbride, MaryPoppins) criticizes(TheodosiaKirkbride, MaryPoppins, 14feb05) happy(TheodosiaKirkbride)  sad(MaryPoppins) happy(TheodosiaKirkbride)  sad(MaryPoppins)  x (is-person(x)  rich(x)   happy(x))  y (is-person(y)  rich(y)  sad(y)) uStandard predicate logic has no inbuilt facilities for other sorts of generalization or propositional structure.

Predicate Logic—The Meat uPredicate logic itself just consists of special symbols such as:        ( )  and the syntax (grammar)—how to structure expressions …  and general rules about the semantics of expressions (their meanings) …  and general procedures for doing deductive inference.  The particular symbols for entities, properties and relationships (e.g., TheodosiaKirkbride, happy, taller-than ), and their meanings,  are up to the particular representation-developer.

Aside: “Symbolic” Systems  “Neural network” systems (= “connectionist” systems) are usually contrasted to “symbolic” systems. Though the real truth is much more complex: for example, a software implementation of an NN is a symbolic system. Some types of NN systems are said to be “subsymbolic”.  But what are “symbolic” systems? One example: systems that represent and reason about things by means of predicate logic. Closely related: systems that use “semantic networks” and “frames” [next major topic in my lectures]. Another example: “rule-based systems” – these manipulate data structures of various sorts (incl. lists and logic-like expressions).