Knowledge Representation

Essential to artificial intelligence are methods of representing knowledge. A number of methods have been developed, including: –Logic : propositional and predicate logic –Semantic Networks –Conceptual Dependencies –Scripts –Frames

Representing Knowledge with Logic Logic systems began with Propositional Calculus in which declarative statements with a truth value of true or false are represented by P,Q,R, etc and combined with logic operators Or, And, Not, If. A sentence such as “Bill must take CSC 2020” is represented by letter P and is true or false. Propositional Calculus was extended to Predicate Calculus by adding Predicates (relations), variables, and quantifiers (For All and There Exists). A sentence such as “Every CS major must take CSC 2020” is represented by “(For All X)( CSMajor(X)  MustTake( CSC2020 ))” Given some facts expressed in either Propositional or Predicate Calculus, new facts or knowledge is inferred by inference rules such as modus ponens or resolution. If the computer can find a path from given facts to a new theorem, the path corresponds to a proof and finding such a path constitutes an example of artificial intelligence

Propositional Logic A declarative statement such as “Bill is a CS student” has a truth value of T or F and is denoted by P (a truth variable) Propositions may be combined with logical operators and the composite statement has value as shown below. –P  Q is true if either P or Q are true and false if both are false –P  Q is true if both P and Q are true and false if either is false. –¬ P is true if P is false and false if P is true –P  Q is true if P and Q have the same truth value and false if their values differ –P  Q is false if P is true and Q is false and true otherwise. A tautology is always true. –P  Q  ¬ P  Q is a tautology. –P  (Q  R)  (P  Q)  (P  R) is a tautology.

Semantic Networks Models meaning of language: –Nodes correspond to word concepts –Arcs are labeled with a property name or relationship and link a node (word concept) with another (value of property). Quillian (1967) introduced semantic networks while others (Simmons -1973, Brachman-1979, Schank-1979) have extended the model.

Semantic Networks Standardization of Relationships Standardization of relationships for representing knowledge expressed in language focuses on case relations between verbs and nouns in sentence (Fillmore ’68, Simmons ’73) Prepositions or articles indicate relationship between verb and noun : –Agent : entity performing the action –Object : entity acted upon –Instrument : entity used in performing the action –Etc.

Conceptual Dependencies Set of Primitive Actions Standardization of relations led to axiomatic approach to build semantic model for representing meaning of language Four Primitive Concept Classes ACTS - ActionsPPs – Objects (Picture producers) AAs – Modifiers of actions (Action Aiders) PAs – Modifiers of objects (picture aiders) Each Action is assumed to reduce to one or more of the primitive ACTs ATRANS – transfer relationship (give) PTRANS – transfer physical location (go) PROPEL MOVE GRASP INGEST EXPEL MTRANS MBUILD CONC SPEAK ATTEND

Building Complex Conceptual Dependencies Conceptual Dependency SemanticsExample PP  ACT An actor acts John  PTRANS … John ran PP  PA Object has attribute John  height John is tall ACT  O PP Indicates object of action John  Propel  O cart John pushes the cart ACT  R  PP   PP Indicates the receipt And donor of An Action John  ATRANS  R  John   Mary John took the book from Mary

Scripts Scripts formalize stereotyped sequences of events. A script for a restaurant differs from one for a “fast food” model. The components of a script are –Entry conditions which must be true for script to be activated –Termination conditions which are true when script is terminated. –Props or object which support the script. The script for a restaurant would include table and cash register props. –Roles are the actions that individual participants must perform. The waiter takes orders, the customer eats and pays bill. –Scenes break the script into subsequences which Are sequential in occurerence Provide alternatives (if condition A then Scene1 elsce Scene2)

Frames Frames formalize stereotyped entities and actions. Frames have labeled slots with slot contents an object or action and slot labels are the role played by the slot filler in relation to the central entity of action. A frame is like a record that contains information relevant to stereotyped action or entity: –Frame Identification –Relationship to other frames (part-of, caused-by) –Slots Label indicating relationship to central slot Requirements for slot filler Procedural information to construct or manipulate slot contents Default Contents Slot contents

Frame Examples Case Frame representation of “Mary fixed the chair with glue” ActionFix AgentMary ObjectChair InstrumentGlue Timepast

Conceptual Graphs A Network Language A conceptual graph is a refinement of semantic networks. A conceptual graph is bipartite with one class of nodes representing word concepts and the other class of nodes representing relations. Arcs go from concept class nodes to relation class nodes and vise vesa.

Conceptual Graph Examples Flies is unary relation or predicate Color is a binary relation Parents is a ternary relation Mary gave john a book bird flies dogcolorbrown childparents mother father mary agent giveobject book recipientjohn