Download e-book for iPad: A System of Logic Ratiocinative and Inductive, Part II (The by John Stuart Mill

By John Stuart Mill

ISBN-10: 0710075065

ISBN-13: 9780710075062

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Additional info for A System of Logic Ratiocinative and Inductive, Part II (The Collected Works of John Stuart Mill - Volume 08)

Sample text

A OR b. s ← not b. ← not q, b. c OR d ← v. ¬c ← not v. u ← z, not p. z ← not u. v ← not w. The goal of this modification is to show how rules, whose literals are not relevant to any cr-rule, can be split. Let U5 be {q, a, b, s, v, w}. Notice that U5 is a splitting set for P5 even though v ∈ U5 and P5 contains the rule c OR d ← v. In fact, v is not relevant to any cr-rule from P5 , and thus c and d are not required to belong to U5 . bU5 (P5 ) is: + [r1 ] q ← not a. a OR b. s ← not b. ← not q, b.

By rule we mean a regular rule or a cr-rule. Given a rule ρ of the form (1) or (2), we call {h1 , . . , hk } the head of the rule, denoted by head(ρ), and {l1 , . . , lm , not lm+1 , . . , not ln } its body, denoted by body(ρ). Also, pos(ρ) denotes {l1 , . . , lm }, neg(ρ) denotes {lm+1 , . . , ln }, name(ρ) denotes name r, and lit(ρ) denotes the set of all literals from ρ. When l ∈ lit(ρ), we say that l occurs in ρ. Splitting a CR-Prolog Program 19 A program is a pair Σ, Π , where Σ is a signature and Π is a set of rules over Σ.

Example. Consider the following scenario. Dr. Amber has configured his mobile phone to decide whether it should ring based on his preferences and context. He has the following preferences: His mobile phone should ring in case of an incoming call (in call) if it is in normal mode (normal) and he is not giving a course lecture (lecture). Dr. Amber is currently located in ’RA201’ university classroom. It is class time, but he has just finished with a lecture and remains in the classroom reading his emails on his laptop.

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A System of Logic Ratiocinative and Inductive, Part II (The Collected Works of John Stuart Mill - Volume 08) by John Stuart Mill

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