KNOWLEDGE REPRESENTATION, REASONING AND DECLARATIVE PROBLEM SOLVING Chitta Baral Arizona State University Tempe, AZ

Introduction Long term goal of this line of research: Make programs, systems, interfaces and agents behave intelligently.

What is intelligence? Some characteristics of intelligent entities: - They can reason. - They can make decisions, and plans. - They can learn. - They can communicate: * take commands, queries, requests, preferences; * act, return answers, plans, decisions, control commands.

Reasoning Reasoning can not be done in vacuum. We need knowledge to reason with. Mathematically, a reasoning task can be expressed as:KB |= Conclusion. Questions: *In what language(s) KB and Conclusion are expressed? *How is |= defined?

Decision making and planning Need data and knowledge to make decisions and plans. Need to be able to express what a valid plan is, and when a decision is optimal or preferred. Thus, need to be able to express preferences and optimality criteria.

Decision making … cont. Questions: * How is knowledge expressed? * How is the goal of a plan expressed? * How are optimality criteria and preferences expressed? * Given data and knowledge what are the options that are enumerated? (How are `models’ defined?)

Learning In what language do we express what is learned? Learning also can not be done (efficiently) in vacuum. Background knowledge and focus are important.

Communication: What vs How? Request for Coffee: the two secretaries. –Secretary1: Sir, there is no water in the coffee pot; what should I do? –Secretary2: Coffee on desk every morning the boss is in; except in summer, when there is a glass of cold water, …

What vs How? How: Exact step by step instructions. What: A high level directive or request whose detailed implementation is left up to the intelligent entity. The more high level the directives and requests an entity can handle … How are the high level directives expressed? Knowledge, and reasoning are also needed to handle them.

The fundamental issue Need appropriate languages to be able to express knowledge, queries, preferences, high-level directives, etc. Recall, KB |= Conclusion. –Syntax for KB and Conclusion. –Semantics that defines ‘|=’. –Semantics: Enumerating the ‘models’ of KB.

Some expected properties of Knowledge Calculus! Must make it easier to add and revise knowledge. –Ordering should not matter that much. –It should be possible that KB |= Concl and KB + New Knowledge |=\= Concl. (This rules out any monotonic logic, such as first- order predicate calculus, to be the language for knowledge representation.)

Some expected properties..cont. Must allow default reasoning. –The Tweety flies example. Birds normally fly. Tweety is a bird. Penguins are birds that do not fly. |= Tweety flies. KB + Tweety is a penguin |= Tweety does not fly. –The airline databases. (Closed world assumption)

Expected properties … cont. Intuitive syntax (for the knowledge writer) –Bird(X) => Flies(X) is often more intuitive than ~Bird(X) V Flies(X). –If-then form seems to be quite intuitive. –Nesting is hard. ( ( ) ( ( ) ) )

Expected properties … cont. Semantics. –Easily definable. –If high complexity, then sound (and useful) approximations. Some structure –Subclasses with different degrees of complexity and expressiveness.

AnsProlog : a possible candidate Syntax: A collection of statements of the form A0 or … or Ak  B1, …, Bm, not C1, … not Cn.

The Tweety example in AnsProlog Fly(X)  Bird(X), not Ab(X). Bird(X)  Penguin(X). Ab(X)  Penguin(X). Bird(tweety). T |= Fly(tweety). T + Penguin(tweety) |= ~ Fly(tweety).

Transitive Closure in AnsProlog ancestor(X,Y)  ancestor(X,Z), parent(Z,Y). ancestor(X,Y)  parent(X,Y). parent(a,b). parent(b,c). parent(c,d). parent(e,f).

Differences with … Prolog: Ordering matters in Prolog; can not handle cycles with not. Logic Programming: It is a class of languages and many different semantics are proposed for not. Classical Logic: –  is not reverse implication. –Disjunction symbol or is non-classical. –The negation as failure symbol not is non-classical. –The classical negation symbol ~ is also used.

Planning: a DPS example. The planning problem. –Actions: puton(X,Y), lift, open, a. –Fluents: on(X,Y), lifted, opened, closed, f. –States: state of the world. Often represented by a set of fluents true in that state. – A simple goal: collection of fluents that need to be true in a state that we want the world to be in.

A simple planning domain initially ~f. initially ~g. b causes f if g. a causes g. finally f. a;b is a plan that achieves the goal.

Planning in AnsProlog. Describing the initial state. ~ holds(f, 1). ~holds(g, 1). Describing effect of actions. holds(f,T+1)  occurs(b,T), holds(g,T). holds(g,T+1)  occurs(a,T). Describing what does not change. holds(f,T+1)  holds(f,T), not ~holds(f,T+1). ~holds(f,T+1)  ~holds(f,T), not holds(f,T+1).

Planning in AnsProlog … cont Enumerating possible plans. other-occurs(A,T)  occurs(B,T), A =\= B. occurs(A,T)  not other-occurs(A,T). Eliminating ‘models’ which do not encode a plan.  not holds(f, plan-length+1). All ‘models’ (answer sets) encode a plan.

Building blocks towards a knowledge calculus. Subclasses and their properties. –Definite, normal, extended, disjunctive. –Acyclic, signed, stratified, call-consistent, order- consistent. Properties –Existence of consistent answer sets. –Existence of unique answer sets. –Complexity of entailment. –Expressibility of the entailment relation. –Relation between the literals in an answer set and the program.

Properties … cont. –Transforming programs. –Equivalence of programs. –Formal relation with other languages. (classical logic, default logic, etc.) –Splitting programs – modular analysis, and computation of answer sets. –Systematic building of programs from components: program composition.

Example Prop. -- Expressibility Normal function-free AnsProlog: Pi 1 P (Co- NP) Function-free AnsProlog: Pi 2 P. AnsProlog: Pi 1 1

Relation between literals in an answer set and the program. If ‘f’ is in an answer set ‘A’ of a program P, then there must be a rule in P such that … If an answer set ‘A’ of a program P satisfies the body of a rule ‘r’ of P then, the head of that rule …

Applications Reasoning –Reasoning with incomplete information, default reasonong. –Reasoning with preferences and priorities, inheritance hierarchies. Declarative problem solving –Planning, job-shop scheduling, tournament scheduling. –Abductive reasoning, explanation generations, diagnosis. –Combinatorial graph problems. –Combinatorial optimizations, combinatorial auctions. –Product configuration.

Applications. (Cont.) Software Engineering: Specification is the program. (rapid prototyping)

Conclusion Representing knowledge and reasoning with it is of fundamental importance in building intelligent entities. AnsProlog is a good candidate for this task. There is now a sizable body of theoretical results, several interpreters, and it has been now used in several applications. This is not my individual work, but has been done by several researchers over the years, most of it in the last ten years.