ai-lect11 - 1 Logical reasoning systems Theorem provers and...

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Unformatted text preview: 1 Logical reasoning systems Theorem provers and logic programming languages Production systems Frame systems and semantic networks Description logic systems 2 Logical reasoning systems Theorem provers and logic programming languages Provers: use resolution to prove sentences in full FOL. Languages: use backward chaining on restricted set of FOL constructs. Production systems based on implications, with consequents interpreted as action (e.g., insertion & deletion in KB). Based on forward chaining + conflict resolution if several possible actions. Frame systems and semantic networks objects as nodes in a graph, nodes organized as taxonomy, links represent binary relations. Description logic systems evolved from semantic nets. Reason with object classes & relations among them. 3 Basic tasks Add a new fact to KB TELL Given KB and new fact, derive facts implied by conjunction of KB and new fact. In forward chaining: part of TELL Decide if query entailed by KB ASK Decide if query explicitly stored in KB restricted ASK Remove sentence from KB: distinguish between correcting false sentence, forgetting useless sentence, or updating KB re. change in the world. 4 Indexing, retrieval & unification Implementing sentences & terms: define syntax and map sentences onto machine representation. Compound: has operator & arguments. e.g., c = P(x) Q(x) Op[c] = ; Args[c] = [P(x), Q(x)] FETCH: find sentences in KB that have same structure as query. ASK makes multiple calls to FETCH. STORE: add each conjunct of sentence to KB. Used by TELL. e.g., implement KB as list of conjuncts TELL(KB, A B) TELL(KB, C D) then KB contains: [A, B, C, D] 5 Complexity With previous approach, FETCH takes O(n) time on n-element KB STORE takes O(n) time on n-element KB (if check for duplicates) Faster solution? 6 Table-based indexing Use hash table to avoid looping over entire KB for each TELL or FETCH e.g., if only allowed literals are single letters, use a 26-element array to store their values.array to store their values....
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ai-lect11 - 1 Logical reasoning systems Theorem provers and...

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