Knowledge Representation and Reasoning (KR):

A vibrant subfield of AI

Jia You

Related Field

• Computational logic

• Constraints/Constraint Programming

• Declarative programming

• Logic programming (not Prolog)

Intelligent Agent

• Can acquire knowledge through various means such as learning from experience, observations, reading, etc., and

• Can reason with this knowledge to make plans, explain observations, achieve goals, etc.

To learn knowledge and to reason with it

• we need to know how to represent knowledge in a computer readable format.

• McCarthy 1959 in Programs with commonsense:

“In order for a program to be capable of learning something it must first be capable of being told it.”

What does KR entail?

• We need languages and corresponding methodologies to represent various kinds of knowledge, and be able to reason with it.

• Forms of reasoning: deduction, abduction, induction, default reasoning, common-sense reasoning, …

Importance of Inventing Suitable KR Languages

Development of a suitable knowledge representation language and methodology is as important to AI systems

as

Calculus is to Physics and Engineering.

What basic properties should a suitable “calculus” of KR possess?

• have a simple and intuitive syntax and semantics;

• allow us to withdraw our conclusions;• allow us to represent and reason with

incomplete information; and• allow us to express and answer problem

solving queries such as planning queries, explanation queries and diagnostic queries.

Inadequacy of first order logic

• It is monotonic: More information one has, more consequences one gets.

• Human communication is typically based on closed world assumption.

An Example of Closed World Assumption

ground-wet watering. ground-wet raining.

• In an open world, there could be other reasons that cause ground-wet (we simply don’t know, or have not said).

• But in a closed world, what we said is all that we know, for Horn clauses, this is called Clark Completion.

Ground-wet watering raining

This is to say …

• We need to study the semantics of KR languages.

Answer Set Programming (ASP)

A program is a collection of rules of form:

A B1, …, Bm, not C1, …, not Cn

where A, Bj and Ck are atoms.

Intended “models” of a program are called answer sets.

Does tweety fly?

• fly(X) bird(X), not ab(X). ab(X) penguin(X). bird(X) penguin(X). bird(tweety).

– We conclude fly(tweety).

• But if we add– penguin(tweety).– We can no longer conclude fly(tweety)

Weight and Cardinality Constraints

• An important extension, where an atom can be a weight/cardinality constraint:

L {a1 = w1, …, an = wn } U where ai are atoms and wj are weights.

E.g. Given a set = {b,c,d,e}, to express all subsets containing a, we can write

a 0 {b,c,d,e} 4 a.

Colorability

Given a map and k colors, is it possible to color the map so that no adjacent regions have the same color?

Represented by a graph:- Each vertex is colored with exactly one color;- no two vertices connected by an edge have the

same color.

A program solving 3-colorability

% Each vertex is colored with exactly one color:

1 {color(V,red), color(V,blue),color(V,yellow) } 1 vertex(V).

% No adjacent vertexes may be colored with the same color.

vertex(V), vertex(U), edge(V,U), isAcolor(C), color(V,C), color(U,C).

Hamiltonian Cycle

Given a set of facts defining the vertices and edges of a directed graph and a starting vertex v0, find a path that visits every vertex exactly once.

Any subset of edges could be on such a path 0 {in(U,V) : edge(U,V) }.

A path must be chained to form a sequence over the edges on it: reachable(V) in(v0,V). reachable(V) reachable(U), in(U,V).

A vertex cannot be visited more than once. edge(U,V), in(U,V), edge(W,V), in(W,V), U W. edge(U,V), in(U,V), edge(U,W), in(U,W), V W.

Don’t forget to say that every vertex must be reached. vertex(U), not reachable(U).

Planning

Represented by a program that expresses:Action choice which action(s) should be chosen at each stateAffected objects the affected objects by an actionEffects if affected, what are the effectsFrame axioms if not affected by any action at a state, the fluents that

hold at the current state remain to hold in the next state.

Is ASP a good candidate?

• Simple syntax• It is non-monotonic.• Can express defaults and their exceptions.• Can represent and reason with incomplete information.• Various implementations: Smodels, DLV, ASSAT, CModels, …• Many applications built using it.• Its initial paper among the top 5 AI source documents in

terms of citeseer citation.

What else we should do about ASP?

• Extensions and semantics;• Need building block results;• The bottleneck: a program may be too large for answer set

computation;• should have systems that can learn knowledge in this

language;• Improving search efficiency - domain dependent knowledge in planning - techniques related to SAT……

Some of resent publications

F Lin and J You. Abductive logic programming by nonground rewrite systems. AAAI-08.

J You and G Liu. Loop formulas for logic programs with arbitrary constraint atoms. AAAI-08.

Y Shen and J You. A generalized Gelfond-Lifschitz transformation for logic programs with abstract constraints. AAAI-07.

G Wu, J You, G Lin. Quartet based phylogeny reconstruction with answer set programming. IEEE/ACM Transactions on Computational Biology and Bioinformatics 2007.

F. Lin and J You. Recycling computed answers in rewrite systems for abduction. ACM Transactions on Computational Logic 2007.

T Janhunen, I. Niemela, D. Seipel, P. Simons, J. You. Unfolding partiality and disjunctions in stable model semantics. ACM Transactions on Computational Logic 2006.