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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Deontic logic ： ウィキペディア英語版 Deontic logic Deontic logic is the field of philosophical logic that is concerned with obligation, permission, and related concepts. Alternatively, a deontic logic is a formal system that attempts to capture the essential logical features of these concepts. Typically, a deontic logic uses ''OA'' to mean ''it is obligatory that A'', (or ''it ought to be (the case) that A''), and ''PA'' to mean ''it is permitted (or permissible) that A''. The term ''deontic'' is derived from the ancient Greek ''déon - δέον'' (gen.: ''δέοντος''), meaning, roughly, ''that which is binding or proper''. ==Standard deontic logic== In von Wright's first system, obligatoriness and permissibility were treated as features of ''acts''. It was found not much later that a deontic logic of ''propositions'' could be given a simple and elegant Kripke-style semantics, and von Wright himself joined this movement. The deontic logic so specified came to be known as "standard deontic logic," often referred to as SDL, KD, or simply D. It can be axiomatized by adding the following axioms to a standard axiomatization of classical propositional logic: : $O(A\; \backslash rightarrow\; B)\; \backslash rightarrow\; (OA\; \backslash rightarrow\; OB)$ : $PA\backslash to\backslash lnot\; O\backslash lnot\; A$ In English, these axioms say, respectively: * If it ought to be that A implies B, then if it ought to be that A, it ought to be that B; * If A is permissible, then it is not the case that it ought not to be that A. ''FA'', meaning it is forbidden that ''A'', can be defined (equivalently) as $O\; \backslash lnot\; A$ or $\backslash lnot\; PA$. There are two main extensions of SDL that are usually considered. The first results by adding an alethic modal operator $\backslash Box$ in order to express the Kantian claim that "ought implies can": : $OA\; \backslash to\; \backslash Diamond\; A.$ where $\backslash Diamond\backslash equiv\backslash lnot\backslash Box\backslash lnot$. It is generally assumed that $\backslash Box$ is at least a KT operator, but most commonly it is taken to be an S5 operator. The other main extension results by adding a "conditional obligation" operator O(A/B) read "It is obligatory that A given (or conditional on) B". Motivation for a conditional operator is given by considering the following ("Good Samaritan") case. It seems true that the starving and poor ought to be fed. But that the starving and poor are fed implies that there are starving and poor. By basic principles of SDL we can infer that there ought to be starving and poor! The argument is due to the basic K axiom of SDL together with the following principle valid in any normal modal logic: :$\backslash vdash\; A\backslash to\; B\backslash Rightarrow\backslash \; \backslash vdash\; OA\backslash to\; OB.$ If we introduce an intensional conditional operator then we can say that the starving ought to be fed ''only on the condition that there are in fact starving'': in symbols O(A/B). But then the following argument fails on the usual (e.g. Lewis 73) semantics for conditionals: from O(A/B) and that A implies B, infer OB. Indeed, one might define the unary operator O in terms of the binary conditional one O(A/B) as $OA\backslash equiv\; O(A/\backslash top)$, where $\backslash top$ stands for an arbitrary tautology of the underlying logic (which, in the case of SDL, is classical). Similarly Alan R. Anderson (1959) shows how to define O in terms of the alethic operator $\backslash Box$ and a deontic constant (i.e. 0-ary modal operator) s standing for some sanction (i.e. bad thing, prohibition, etc.): $OA\backslash equiv\backslash Box(\backslash lnot\; A\backslash to\; s)$. Intuitively, the right side of the biconditional says that A's failing to hold necessarily (or strictly) implies a sanction. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Deontic logic」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.