Download PDF by Witold Lukaszewicz: Non-Monotonic Reasoning: Formalization of Commonsense

By Witold Lukaszewicz

ISBN-10: 0136244467

ISBN-13: 9780136244462

From preface: Non-monotonic reasoning could be loosely defined because the strategy of drawing conclusions that could be invalidated through new info. as a result of its shut dating to human commonsense reasoning, non-monotonic inference has turn into one of many significant study themes within the box of man-made intelligence (AI).

I have tried to accomplish pursuits in penning this publication. One used to be to give an explanation for what non-monotonic reasoning is and the way it's been approached within the AI examine. the opposite used to be to supply an in depth examine of the main influential non-monotonic logics. The ebook is basically addressed to scholars and learn employees in AI (and comparable disciplines), yet also needs to be beneficial to practitioners thinking about specialist and clever knowledge-based platforms.

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33 (Compactness Theorem) A theory T has a model iff each Finite subtheory of T has a model. f In particular, A is a semantic consequence of the predicate calculus (over L), written \=A, iff A is true in every frame (for L)} | If T \= A, then we also say that A {logically) follows from T, A is entailed by T, or T entails A. 34 Let T consist of the following axioms: Bird(Tweety) Vx. Bird{x) => Flies{x) Vx. Flies{x) zd Ffas- Wings{x) +The notation T \= A was given a somewhat different meaning in the previous section, where T was a propositional theory.

It is easily seen that the restriction to alphabets with computable sets of predicate and function constants guarantees the computability of any first-order language. L al is said to be a first-order language with equality iff ‘ = ’ e AL; otherwise, L al is said to be a first-order language without equality. We use the letters A, B, C and D (resp. a, /? and y), possibly with subscripts and/or primes, as syntactic variables ranging over formulae (resp. terms). Formulae of the form (—|/l)and (A =d B) have the same meaning as in propositional logic.

The former is a connective which may occur in formulae; the latter is a meta-language symbol which is used to speak about formulae. Sec. 2] Step 2. CLASSICAL PROPOSITIONAL LOGIC 31 Move —i inward. In the formula obtained in Step 1, replace —i(B a B by by by — { B v C) C) ^ -iB — i a —iC —B v -nC B until all occurrences of —i immediately precede atomic formulae. Step 3. Distribute possible (B B C) a v (C a v a over D D) v . In the formula constructed in Step 2, replace as long as by by (B (B v D) a (C v v C) a (B v D) D) and denote the resulting formula by A .

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Non-Monotonic Reasoning: Formalization of Commonsense Reasoning by Witold Lukaszewicz

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