Knowledge Representation and Reasoning - Villanova University 维拉诺瓦大学知识表示与推理

– On (x, z, s) Clear (x, s) On (x, table, Result(Move(x, table), s)) On(x, z, Result (Move (x, table), s))
– On (y, z, s) y x On (y, z, Result (Move (x, table), s)) – The proliferation of frame axioms becomes very cumbersome in
Systems that reason with causal rules are called model-based reasoning systems – Diagnostic rules infer the presence of hidden properties directly from the percept-derived information. We have already seen two diagnostic rules:
– Causal rules reflect the assumed direction of causality in the world:
(Al1,l2,s) At(Wumpus,l1,s) ^ Adjacent(l1,l2) => Smelly(l2) (A l1,l2,s) At(Pit,l1,s) ^ Adjacent(l1,l2) => Breezy(l2)
• Situation calculus is another way • A situation is a snapshot of the world at some
instant in time • When the agent performs an action A
in situation S1, the result is a new situation S2.
– Logic programming languages – Theorem provers – Rule-based or production systems – Semantic networks – Frame-based representation languages – Databases (deductive, relational, object-oriented, etc.) – Constraint reasoning systems – Description logics – Bayesian networks – Evidential reasoning
theory, fuzzy reasoning
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Introduction
• Real knowledge representation and reasoning systems come in several major varieties.
• These differ in their intended use, expressivity, features,… • Some major families are
• but sometimes a square can be OK even when smells and breezes abound. Consider the following model-based rule:
(x,t) ( t(Wumpus,x,t) ^ Pit(x)) <=> OK(x)
(A l,s) At(Agent,l,s) ^ Breeze(s) => Breezy(l) (A l,s) At(Agent,l,s) ^ Stench(s) => Smelly(l)
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Representing change: The frame problem
• Frame axiom: If property x doesn’t change as a result of applying action a in state s, then it stays the same.
– Forward-chaining production rule systems – Semantic networks – Frame-based systems – Description logics
• Abductive/uncertain methods
– What’s abduction? – Why do we need uncertainty? – Bayesian reasoning – Other methods: Default reasoning, rule-based methods, Dempster-Shafer
• Example: The action agent-walks-to-location-y could be represented by
– (x)(y)(s) (at(Agent,x,s) ^ ~onbox(s)) -> at(Agent,y,result(walk(y),s))
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Deducing hidden properties
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Ontological Engineering
• Structuring knowledge in a useful fashion • An ontology formally represents concepts in a domain and
relationships between those concepts • Using the proper representation is key!
Adapted from slides by Tim Finin and Marie desJardins.
Some material adopted from notes
by Andreas Geyer-Schulz, and Chuck Dyer.
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Outline
• Approaches to knowledge representation • Situation calculus • Deductive/logical methods
– It can be the difference between success and failure
• Often costly to formally engineer domain knowledge
– Domain experts (a.k.a. subject matter experts) – Commercial ontology, e.g. Cyc (cyc/, /)
• If the axioms correctly and completely describe the way the world works and the way percepts are produced, the inference procedure will correctly infer the strongest possible description of the world state given the available percepts.
situation s.” E.g., holds(at(hunter,1,1),s0)
• Add a new function, result(a,s), that maps a situation s into a new situation as a result of performing action a. For example, result(forward, s) is a function that returns the successor state (situation) to s
Knowledge Representation and
Reasoning
Focus on Sections 10.1-10.3, 10.6
Guest Lecturer: Eric Eaton
University of Maryland Baltimore County Lockheed Martin Advanced Technology Laboratories
• Neither Breezy nor Smelly need situation arguments because pits and Wumpuses do not move arouI
• Why both causal and diagnostic rules? Maybe diagnostic rules are enough? However, it is very tricky to ensure that they derive the strongest possible conclusions from the available information.
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Situations
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Situation calculus
• A situation is a snapshot of the world at an interval of time during which nothing changes
• Every true or false statement is made with respect to a particular situation.
– Add situation variables to every predicate. – at(hunter,1,1) becomes at(hunter,1,1,s0): at(hunter,1,1) is true in situation (i.e., state)
s0. – Alternatively, add a special 2nd-order predicate, holds(f,s), that means “f is true in