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  B 1, …, B m, not C 1, …, not C n where A, B j and C k 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 v 0, 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(v 0,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 state Affected objects the affected objects by an action Effects if affected, what are the effects Frame 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 F. Lin and J You. Recycling computed answers in rewrite systems for abduction. ACM Transactions on Computational Logic T Janhunen, I. Niemela, D. Seipel, P. Simons, J. You. Unfolding partiality and disjunctions in stable model semantics. ACM Transactions on Computational Logic 2006.