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| The '''situation calculus''' is a [[logic]] formalism designed for representing and reasoning about dynamical domains. It was first introduced by [[John McCarthy (computer scientist)|John McCarthy]] in 1963. The main version of the situational calculus that is presented in this article is based on that introduced by [[Ray Reiter]] in 1991. It is followed by sections about McCarthy's 1986 version and a [[logic programming]] formulation.
| | == 「報告書......私は == |
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| == Overview == | | ほとんど未定躊躇し、彼は突然そう暗くない場合がございます [http://www.dmwai.com/webalizer/kate-spade-5.html ケイトスペード バッグ 激安]。<br><br>は 'あなたは賢い男だ、そうでなければ、彼らはそう長く生きられないだろう......あなたは私たちが実際にあなたが何をしているか知っている、私たちが必要なものを知っている、とは関係ありませんが小さすぎるいくつかの小さなミス、誰かが私たちの兄弟を突くことができ、私たちは、あなたが感じるようになる彼？「MA鵬タオは、炉を降りないで、次の馬鞍山を振り返った。<br>「いいえ、でも本当に私はしませんでした。」<br>馬鞍山鉄鋼炉の道、マサチューセッツ鵬は少しびくびく参照した。<br><br>「どのように好意とにかく、彼は火の中にパンのように [http://www.dmwai.com/webalizer/kate-spade-13.html kate spade ハンドバッグ]？、あなたが瓦礫の下に心だ？とにかく、これはまた、あなたはまだ準備ができて、ダウンしてバックアップしていると、彼は一緒に落ちた？とにかく、彼は遅かれ早かれそれを説明する必要があります、あなたは警察の追跡を聞かせする準備が整いました可能でない場合には、私たちは彼の証拠を移動することはできませんが、今、動きはすぐに覆さ [http://www.dmwai.com/webalizer/kate-spade-6.html ケイトスペード 財布 セール]？あなたのために開催しています。「MA鵬は、単語のタッチが、脅威が非常に強いです、彼は知っており、これらの人々が言うことができない、と述べので、唯一の感覚 [http://www.dmwai.com/webalizer/kate-spade-11.html バッグ ケイトスペード]。<br><br>は馬鞍山鉄鋼炉の不確実な本物の [http://www.dmwai.com/webalizer/kate-spade-11.html バッグ ケイトスペード] '私は...... ......ポイントの状況を知っているが、と思います」。<br>その上<br>「報告書......私は |
| | 相关的主题文章： |
| | <ul> |
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| | <li>[http://gtjt.gaotang.cn/plus/feedback.php?aid=45 http://gtjt.gaotang.cn/plus/feedback.php?aid=45]</li> |
| | |
| | <li>[http://www.nationalfootwear.com/cgi-bin/shop/commerce.cgi http://www.nationalfootwear.com/cgi-bin/shop/commerce.cgi]</li> |
| | |
| | <li>[http://www.maxpokerclubs.com/forum.php?mod=viewthread&tid=126140 http://www.maxpokerclubs.com/forum.php?mod=viewthread&tid=126140]</li> |
| | |
| | </ul> |
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| The situation calculus represents changing scenarios as a set of [[first-order logic]] formulae. The basic elements of the calculus are:
| | == 警察はまた、警察の問題である場合によ == |
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| *The actions that can be performed in the world
| | 私たちはここで良い練習を来もたらしますか？ [http://www.dmwai.com/webalizer/kate-spade-9.html ケイトスペードバッグセール] '<br>警察はまた、警察の問題である場合によ<br>、この判断は良いですが、少なくとも、突然のすべての人の心のしゃっくりの強打を聞かせて、通常の言葉と行動で、本当に深刻な問題であり、私たちは次の、李のErドン軽蔑を凍結し、まっすぐ進む：「あなたがたの自己ヶ月行くとき地獄、ああ、あなたは今の警察官、通常以上の200から1入院の数の割合、つまり、警察が1つを選ぶことはできませんので、そこに数万人を過ごすこのグループが1つを結ばせて雇用知って......私達はまた南にそれを持って来るためにお金を使うことのように？また、あなたの問題を解決する？あなたの問題に対する最適なソリューションを、解決し、何よりもずっと速く、あなたの食事ポンプ場を、オフにしてください。 [http://www.dmwai.com/webalizer/kate-spade-11.html ケイトスペードニューヨーク 財布] '<br>彼が主張したよう<br>がああです、それは意味がない、決定的な、最終的な目は学校での懲戒罰を避けるために、罪の上に戻って非常に少なくとも最年少ふしだらな女、問題となっていることもある非常に正確を見て、じっと誰も存在しない、と述べ規律検査チームを繰り返し壮大な、呉Guangyuは、彼はゆっくりと突く最寄り尋ね:.罪よりも食べて [http://www.dmwai.com/webalizer/kate-spade-2.html マザーズバッグ ケイトスペード] 'あなたは、私たちは皆、どのようにあなたについて見てゆうの子、。'<br>上昇を<br> |
| *The [[Fluent (artificial intelligence)|fluents]] that describe the state of the world
| | 相关的主题文章： |
| *The situations
| | <ul> |
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| | <li>[http://st-anna.com/cgi-bin/fantasy.cgi http://st-anna.com/cgi-bin/fantasy.cgi]</li> |
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| | <li>[http://www.hxhtz.net/plus/feedback.php?aid=110 http://www.hxhtz.net/plus/feedback.php?aid=110]</li> |
| | |
| | <li>[http://melody.lib.net/game/bbs/honey/keijiban_n1.cgi http://melody.lib.net/game/bbs/honey/keijiban_n1.cgi]</li> |
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| | </ul> |
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| A domain is formalized by a number of formulae, namely:
| | == ピープルコーディネート == |
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| *Action precondition axioms, one for each action
| | ピープルコーディネート。 '<br><br>「郊外支店カン丁戻って郊外の分岐処理へのあなたのすべての二十から三4を担当するグループを [http://www.dmwai.com/webalizer/kate-spade-7.html ケイトスペードのバッグ]。<br><br>'陳ヤングループどこで必要性の証拠には、8 7にしています。'<br><br>「重ケースチーム周フアングループは、あなたが一から十まで、フォレンジックを持っている。 [http://www.dmwai.com/webalizer/kate-spade-14.html kate spade マザーズバッグ] '<br><br>「重ケースチームドンShaojunグループが、あなたは、13にフォレンジックを持っている。 '<br><br>「隊郭Jinlinグループ、14階建て、背中隊に、17ギャンブルがある。 [http://www.dmwai.com/webalizer/kate-spade-7.html ケイトスペード かごバッグ] '<br>SWATチーム制御による事前のサイトを通じてセキュリティ廊下から層によるhuanhangrn層、層お辞儀ヘッドの男性と女性の層はより複雑とケース、容疑者に関与していないが、その後の警察に分離されている道を急いでされている [http://www.dmwai.com/webalizer/kate-spade-8.html kate spade 財布 ゴールド]。<br><br>Xipixiaolianフラットが、Xiaomeng Qiはあなたが本当にそれを指揮することを発見するが、私は心を罪では、これらの使い捨て警察彼は非常によく組織ことは明らかである。<br><br>「ワンコール、、あなたが繰り返しつながった上記のように [http://www.dmwai.com/webalizer/kate-spade-8.html ケイトスペード ハンドバッグ]......階下の心をインタビューするために一つの......階下記者に電話 |
| *Successor state axioms, one for each fluent
| | 相关的主题文章： |
| *Axioms describing the world in various situations
| | <ul> |
| *The foundational axioms of the situation calculus
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| | <li>[http://ccuaer.cuew.com/plus/feedback.php?aid=60 http://ccuaer.cuew.com/plus/feedback.php?aid=60]</li> |
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| | <li>[http://WWW.h5230.cn/forum.php?mod=viewthread&tid=39650&extra= http://WWW.h5230.cn/forum.php?mod=viewthread&tid=39650&extra=]</li> |
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| | <li>[http://bbs.xiaocaocms.com/forum.php?mod=viewthread&tid=1155342 http://bbs.xiaocaocms.com/forum.php?mod=viewthread&tid=1155342]</li> |
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| | </ul> |
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| A simple robot world will be modeled as a running example. In this world there is a single robot and several inanimate objects. The world is laid out according to a grid so that locations can be specified in terms of <math>(x,y)</math> coordinate points. It is possible for the robot to move around the world, and to pick up and drop items. Some items may be too heavy for the robot to pick up, or fragile so that they break when they are dropped. The robot also has the ability to repair any broken items that it is holding.
| | == 'あなたは非常に理解したのか == |
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| == Elements == | | 見て？ 'シャオ元帥は突然尋ねた。<br><br>「私は、彼は私たちの政治的なクラスであることを初めて、私たちの先生は言った......非常に悲劇的なケースは、誰が結果の種別になりたかったん卒業するまでの時間を持っている。 [http://www.dmwai.com/webalizer/kate-spade-8.html ケイトスペード ハンドバッグ] 'ドゥーリトル、それは静かに言った少年は不思議尋ね憂鬱視線を見て： [http://www.dmwai.com/webalizer/kate-spade-0.html ケイトスペード バッグ] 'あなたは私はあなたが住んでいると思います行くときラムズ、市はその年の生存率は、実際にあなたが良い行われますが、なぜ最後の最後で、それを与えるように選ぶのか？。'<br><br>その年、誰も生存能力を破ったとき人はジレンマに強制されていることを考えなかった他の多くの貧しいよりも良い健闘、シャオ元帥は生活の調停を拾う、非常に驚くべきものだ、シャオ元帥は微笑んで言った： [http://www.dmwai.com/webalizer/kate-spade-2.html ケイトスペード 財布 店舗] 「私は知っているので、徐Pingqiuが人に特別なタスクを募集、私はあまりにもよく、彼らの方法に作用しています。 '<br><br>'あなたは非常に理解したのか [http://www.dmwai.com/webalizer/kate-spade-6.html kate spade マザーズバッグ]？'ドゥーリトルは、最大変だった。<br><br>「ああ、はい、警察は、時にはそれらの犯罪者の差よりもレベルの詐欺 [http://www.dmwai.com/webalizer/kate-spade-3.html ケイトスペード バッグ 通販]。」シャオ元帥の道。<br><br>ドゥーリトルは、笑っていた、その年は、貧しい子供たちのグループは、すべてがされていると言わなければならない |
| | 相关的主题文章： |
| | <ul> |
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| | <li>[http://www.bev-t-boo.com/cgi-bin/guestbook/guestbook.cgi http://www.bev-t-boo.com/cgi-bin/guestbook/guestbook.cgi]</li> |
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| | <li>[http://www.ecoolr.com/plus/feedback.php?aid=472 http://www.ecoolr.com/plus/feedback.php?aid=472]</li> |
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| | <li>[http://www.ahyancheng.com/plus/feedback.php?aid=41 http://www.ahyancheng.com/plus/feedback.php?aid=41]</li> |
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| | </ul> |
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| The main elements of the situation calculus are the actions, the fluents, and the situations. A number of objects are also typically involved in the description of the world. The situation calculus is based on a sorted domain with three sorts: actions, situations, and objects, where the objects include everything that is not an action or a situation. Variables of each sort can be used. While actions, situations, and objects are elements of the domain, the fluents are modeled as either predicates or functions.
| | == like minds in general == |
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| ===Actions===
| | My big mistake. '<br><br>like minds in general, Xu Pingqiu Carter, Lin Yu Jing that the Department of grotesque frequency chirp phone rang again, [http://www.dmwai.com/webalizer/kate-spade-13.html ケイトスペード バッグ ショルダー] and this time surprised the police discovered that the outcome of the decision today night, this is [http://www.dmwai.com/webalizer/kate-spade-11.html ケイトスペードのバッグ] not the [http://www.dmwai.com/webalizer/kate-spade-3.html ケイトスペード ショルダーバッグ] notorious Xu Detective, but that does not know where to hide in the inside, it is a grenade fired into the enemy camp, the camp will be strong again ripped, destroyed .........<br><br>'How far are you from the target?' Xu Pingqiu anxiously asked.<br><br>'I do not know, anyway, far away ...... Damn, this smelly bitch lied to me one back, get her to get back.'<br><br>each other fiercely, and now, the phrase rogue flavor if nobody laughed, but also pleasant to speak, than the sounds of nature, to seize a drug dealer, that's [http://www.dmwai.com/webalizer/kate-spade-6.html ケイトスペード 財布 セール] enough to rank all shiny things, even if only a participant identity, but also feel that this is a non-noble glory, this time, in front of everyone, and [http://www.dmwai.com/webalizer/kate-spade-14.html ケイトスペード時計人気] who on spiritual resonance, and have the same thoughts:<br><br>this bitch ...... get back! |
| | | 相关的主题文章： |
| The actions form a sort of the domain. Variables of sort action can be used. Actions can be quantified. A special predicate <math>Poss</math> is used to indicate when an action is executable.
| | <ul> |
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| In the example robot world, possible action terms would be <math>move(x,y)</math> to model the robot moving to a new location <math>(x,y)</math>, and <math>pickup(o)</math> to model the robot picking up an object <math>o</math>.
| | <li>[http://www.4006908516.com/plus/feedback.php?aid=38 http://www.4006908516.com/plus/feedback.php?aid=38]</li> |
| | | |
| ===Situations===
| | <li>[http://www.parfa.jp/index.cgi http://www.parfa.jp/index.cgi]</li> |
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| In the situation calculus, a dynamic world is modeled as progressing through a series of situations as a result of various actions being performed within the world. A situation represents a history of action occurrences. In the Reiter version of the situation calculus described here, a situation does not represent a state, contrarily to the literal meaning of the term and contrarily to the original definition by McCarthy and Hayes. This point has been summarized by Reiter as follows:
| | <li>[http://www.cherumo.net/bbs/ibbs.cgi http://www.cherumo.net/bbs/ibbs.cgi]</li> |
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| : A situation is a finite sequence of actions. Period. It's not a state, it's not a snapshot, it's a ''history'' [http://www.ida.liu.se/ext/etai/rac/notes/1997/09/note.html].
| | </ul> |
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| The situation before any actions have been performed is typically denoted <math>S_0</math> and called the initial situation. The new situation resulting from the performance of an action is denoted using the function symbol <math>do</math> (Some other references also use <math>result</math>). This function symbol has a situation and an action as arguments, and a situation as a result, the latter being the situation that results from performing the given action in the given situation.
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| The fact that situations are sequences of actions and not states is enforced by an axiom stating that <math>do(a,s)</math> is equal to <math>do(a',s')</math> if and only if <math>a=a'</math> and <math>s=s'</math>. This condition makes no sense if situations were states, as two different actions executed in two different states can result in the same state.
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| In the example robot world, if the robot's first action is to move to location <math>(2,3)</math>, the first action is <math>move(2,3)</math> and the resulting situation is <math>do(move(2,3),S_{0})</math>. If its next action is to pick up the ball, the resulting situation is <math>do(pickup(Ball),do(move(2,3),S_{0}))</math>. Situations terms like <math>do(move(2,3),S_{0})</math> and <math>do(pickup(Ball),do(move(2,3),S_{0}))</math> denote the sequences of executed actions, and not the description of the state that result from execution.
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| === Fluents ===
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| Statements whose [[truth value]] may change are modeled by ''relational fluents'', predicates which take a situation as their final argument. Also possible are ''functional fluents'', functions which take a situation as their final argument and return a situation-dependent value. Fluents may be thought of as "properties of the world"'.
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| In the example, the fluent <math>is\_ carrying(o,s)</math> can be used to indicate that the robot is carrying a particular object in a particular situation. If the robot initially carries nothing, <math>is\_ carrying(Ball,S_{0})</math> is false while <math>is\_ carrying(Ball,do(pickup(Ball),S_{0}))</math> is true. The location of the robot can be modeled using a functional fluent <math>location(s)</math> which returns the location <math>(x,y)</math> of the robot in a particular situation.
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| ==Formulae==
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| The description of a dynamic world is encoded in [[Second-order_logic|second order logics]] using three kinds of formulae: formulae about actions (preconditions and effects), formulae about the state of the world, and foundational axioms.
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| ===Action preconditions===
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| Some actions may not be executable in a given situation. For example, it is impossible to put down an object unless one is in fact carrying it. The restrictions on the performance of actions are modeled by literals of the form <math>Poss(a,s)</math>, where <math>a</math> is an action, <math>s</math> a situation, and <math>Poss</math> is a special binary predicate denoting executability of actions. In the example, the condition that dropping an object is only possible when one is carrying it is modeled by:
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| <math> | |
| Poss(drop(o),s)\leftrightarrow is\_ carrying(o,s)
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| </math> | |
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| As a more complex example, the following models that the robot can carry only one object at a time, and that some objects are too heavy for the robot to lift (indicated by the predicate <math>heavy</math>):
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| <math>
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| Poss(pickup(o),s)\leftrightarrow(\forall z\neg is\_ carrying(z,s))\wedge\neg heavy(o)
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| </math>
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| ===Action effects===
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| Given that an action is possible in a situation, one must specify the effects of that action on the fluents. This is done by the effect axioms. For example, the fact that picking up an object causes the robot to be carrying it can be modeled as:
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| <math>
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| Poss(pickup(o),s)\rightarrow is\_ carrying(o,do(pickup(o),s))
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| </math>
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| It is also possible to specify conditional effects, which are effects that depend on the current state. The following models that some objects are fragile (indicated by the predicate <math>fragile</math>) and dropping them causes them to be broken (indicated by the fluent <math>broken</math>):
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| <math>
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| Poss(drop(o),s)\wedge fragile(o)\rightarrow broken(o,do(drop(o),s))
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| </math>
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| While this formula correctly describes the effect of the actions, it is not sufficient to correctly describe the action in logic, because of the [[frame problem]].
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| ===The frame problem===
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| While the above formulae seem suitable for reasoning about the effects of actions, they have a critical weakness - they cannot be used to derive the ''non-effects'' of actions. For example, it is not possible to deduce that after picking up an object, the robot's location remains unchanged. This requires a so-called frame axiom, a formula like:
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| <math>
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| Poss(pickup(o),s)\wedge location(s)=(x,y)\rightarrow location(do(pickup(o),s))=(x,y)
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| </math>
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| The need to specify frame axioms has long been recognised as a problem in axiomatizing dynamic worlds, and is known as the [[frame problem]]. As there are generally a very large number of such axioms, it is very easy for the designer to leave out a necessary frame axiom, or to forget to modify all appropriate axioms when a change to the world description is made.
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| ===The successor state axioms===
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| The successor state axioms "solve" the frame problem in the situation calculus. According to this solution, the designer must enumerate as effect axioms all the ways in which the value of a particular fluent can be changed. The effect axioms affecting the value of fluent <math>F(\overrightarrow{x},s)</math> can be written in generalised form as a positive and a negative effect axiom:
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| <math>
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| Poss(a,s)\wedge\gamma_{F}^{+}(\overrightarrow{x},a,s)\rightarrow F(\overrightarrow{x},do(a,s))
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| </math>
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| <math>
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| Poss(a,s)\wedge\gamma_{F}^{-}(\overrightarrow{x},a,s)\rightarrow\neg F(\overrightarrow{x},do(a,s))
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| </math>
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| The formula <math>\gamma_{F}^{+}</math> describes the conditions under which action <math>a</math> in situation <math>s</math> makes the fluent <math>F</math> become true in the successor situation <math>do(a,s)</math>. Likewise, <math>\gamma_{F}^{-}</math> describes the conditions under which performing action <math>a</math> in situation <math>s</math> makes fluent <math>F</math> false in the successor situation.
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| If this pair of axioms describe all the ways in which fluent <math>F</math> can change value, they can be rewritten as a single axiom:
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| <math>
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| Poss(a,s)\rightarrow\left[F(\overrightarrow{x},do(a,s))\leftrightarrow\gamma_{F}^{+}(\overrightarrow{x},a,s)\vee\left(F(\overrightarrow{x},s)\wedge\neg\gamma_{F}^{-}(\overrightarrow{x},a,s)\right)\right]
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| </math>
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| In words, this formula states: "given that it is possible to perform action <math>a</math> in situation <math>s</math>, the fluent <math>F</math> would be true in the resulting situation <math>do(a,s)</math> if and only if performing <math>a</math> in <math>s</math> would make it true, or it is true in situation <math>s</math> and performing <math>a</math> in <math>s</math> would not make it false."
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| By way of example, the value of the fluent <math>broken</math> introduced above is given by the following successor state axiom:
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| <math>
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| Poss(a,s) \rightarrow \left[ broken(o,do(a,s)) \leftrightarrow a=drop(o)\wedge fragile(o)
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| \vee broken(o,s) \wedge a \neq repair(o) \right]
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| </math>
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| ===States===
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| The properties of the initial or any other situation can be specified by simply stating them as formulae. For example, a fact about the initial state is formalized by making assertions about <math>S_{0}</math> (which is not a state, but a ''situation''). The following statements model that initially, the robot carries nothing, is at
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| location <math>(0,0)</math>, and there are no broken objects:
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| <math>
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| \forall z\,\neg is\_ carrying(z,S_{0})
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| </math>
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| <math>
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| location(S_{0})=(0,0)\,
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| </math>
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| <math>
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| \forall o\,\neg broken(o,S_{0})
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| </math>
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| ===Foundational axioms===
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| The foundational axioms of the situation calculus formalize the idea that situations are histories by having <math>do(a,s)=do(a',s') \iff a=a' \and s=s'</math>. They also include other properties such as the second order induction on situations.
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| ==Regression==
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| Regression is a mechanism for proving consequences in the situation calculus. It is based on expressing a formula containing the situation <math>do(a,s)</math> in terms of a formula containing the action <math>a</math> and the situation <math>s</math>, but not the situation <math>do(a,s)</math>. By iterating this procedure, one can end up with an equivalent formula containing only the initial situation <math>S_0</math>. Proving consequences is supposedly simpler from this formula than from the original one.
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| ==GOLOG==
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| GOLOG is a logic programming language based on the situation calculus.
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| ==The original version of the situation calculus==
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| The main difference between the original situation calculus by McCarthy and Hayes and the one in use today is the interpretation of situations. In the modern version of the situational calculus, a situation is a sequence of actions. Originally, situations were defined as “the complete state of the universe at an instant of time”. It was clear from the beginning that such situations could not be completely described; the idea was simply to give some statements about situations, and derive consequences from them. This is also different from the approach that is taken by the [[fluent calculus]], where a state can be a collection of known facts, that is, a possibly ''incomplete'' description of the universe.
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| In the original version of the situation calculus, fluents are not reified. In other words, conditions that can change are represented by predicates and not by functions. Actually, McCarthy and Hayes defined a fluent as a function that depends on the situation, but they then proceeded always using predicates to represent fluents. For example, the fact that it is raining at place <math>x</math> in the situation <math>s</math> is represented by the literal <math>raining(x,s)</math>. In the 1986 version of the situation calculus by McCarthy, functional fluents are used. For example, the position of an object <math>x</math> in the situation <math>s</math> is represented by the value of <math>location(x,s)</math>, where <math>location</math> is a function. Statements about such functions can be given using equality: <math>location(x,s)=location(x,s')</math> means that the location of the object <math>x</math> is the same in the two situations <math>s</math> and <math>s'</math>.
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| The execution of actions is represented by the function <math>result</math>: the execution of the action <math>a</math> in the situation <math>s</math> is the situation <math>result(a,s)</math>. The effects of actions are expressed by formulae relating fluents in situation <math>s</math> and fluents in situations <math>result(a,s)</math>. For example, that the action of opening the door results in the door being open if not locked is represented by:
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| :<math>\neg locked(door,s) \rightarrow open(door, result(opens,s))</math>
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| The predicates <math>locked</math> and <math>open</math> represent the conditions of a door being locked and open, respectively. Since these condition may vary, they are represented by predicates with a situation argument. The formula says that if the door is not locked in a situation, then the door is open after executing the action of opening, this action being represented by the constant <math>opens</math>.
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| These formulae are not sufficient to derive everything that is considered plausible. Indeed, fluents at different situations are only related if they are preconditions and effects of actions; if a fluent is not affected by an action, there is no way to deduce it did not change. For example, the formula above does not imply that <math>\neg locked(door,result(opens,s))</math> follows from <math>\neg locked(door,s)</math>, which is what one would expect (the door is not made locked by opening it). In order for inertia to hold, formulae called ''frame axioms'' are needed. These formulae specify all non-effects of actions:
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| :<math>\neg locked(door,s) \rightarrow \neg locked(door, result(opens,s))</math>
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| In the original formulation of the situation calculus, the initial situation, later denoted by <math>S_0</math>, is not explicitly identified. The initial situation is not needed if situations are taken to be descriptions of the world. For example, to represent the scenario in which the door was closed but not locked and the action of opening it is performed is formalized by taking a constant <math>s</math> to mean the initial situation and making statements about it (e.g., <math>\neg locked(door,s)</math>). That the door is open after the change is reflected by formula <math>open(door,result(opens,s))</math> being entailed. The initial situation is instead necessary if, like in the modern situation calculus, a situation is taken to be a history of actions, as the initial situation represents the empty sequence of actions.
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| The version of the situation calculus introduced by McCarthy in 1986 differs to the original one for the use of functional fluents (e.g., <math>location(x,s)</math> is a term representing the position of <math>x</math> in the situation <math>s</math>) and for an attempt to use [[Circumscription (logic)|circumscription]] to replace the frame axioms.
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| ==The situation calculus as a logic program==
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| It is also possible (e.g. Kowalski 1979, Apt and Bezem 1990, Shanahan 1997) to write the situation calculus as a logic program:
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| <math>Holds(f, do(a, s)) \leftarrow Poss(a, s) \wedge Initiates(a, f, s)</math>
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| <math>Holds(f, do(a, s)) \leftarrow Poss(a, s) \wedge Holds(f, s) \wedge \neg Terminates(a, f, s)</math> | |
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| Here <math>Holds</math> is a meta-predicate and the variable <math>f</math> ranges over fluents. The predicates <math>Poss</math>, <math>Initiates</math> and <math>Terminates</math> correspond to the predicates <math>Poss</math>, <math>\gamma_{F}^{+}(\overrightarrow{x},a,s)</math>, and <math>\gamma_{F}^{-}(\overrightarrow{x},a,s)</math> respectively. The left arrow <math>\leftarrow</math> is half of the equivalence <math>\leftrightarrow</math>. The other half is implicit in the completion of the program, in which negation is interpreted as [[negation as failure]]. Induction axioms are also implicit, and are needed only to prove program properties. Backward reasoning as in [[SLD resolution]], which is the usual mechanism used to execute logic programs, implements regression implicitly.
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| ==See also==
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| * [[Frame problem]]
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| * [[Event calculus]]
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| == References ==
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| * J. McCarthy and P. Hayes (1969). [http://www-formal.stanford.edu/jmc/mcchay69.html Some philosophical problems from the standpoint of artificial intelligence]. In B. Meltzer and D. Michie, editors, ''Machine Intelligence'', 4:463–502. Edinburgh University Press, 1969.
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| * R. Kowalski (1979). Logic for Problem Solving - Elsevier North Holland.
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| * K.R. Apt and M. Bezem (1990). Acyclic Programs. In: 7th International Conference on Logic Programming. MIT Press. Jerusalem, Israel.
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| * R. Reiter (1991). The frame problem in the situation calculus: a simple solution (sometimes) and a completeness result for goal regression. In Vladimir Lifshitz, editor, ''Artificial intelligence and mathematical theory of computation: papers in honour of John McCarthy'', pages 359–380, San Diego, CA, USA. Academic Press Professional, Inc. 1991.
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| * M. Shanahan (1997). Solving the Frame Problem: a Mathematical Investigation of the Common Sense Law of Inertia. MIT Press.
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| * H. Levesque, F. Pirri, and R. Reiter (1998). [http://www.ep.liu.se/ej/etai/1998/005 Foundations for the situation calculus]. ''[[Electronic Transactions on Artificial Intelligence]]'', 2(3–4):159-178.
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| * F. Pirri and R. Reiter (1999). Some contributions to the metatheory of the Situation Calculus. ''[[Journal of the ACM]]'', 46(3):325–361. {{doi|10.1145/316542.316545}}
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| * R. Reiter (2001). Knowledge in Action: Logical Foundations for Specifying and Implementing Dynamical Systems. The MIT Press.
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