From 13e6195c4e19a0227ae2b4770d9221e73fcdee7e Mon Sep 17 00:00:00 2001 From: Robert Jeutter Date: Mon, 5 Jul 2021 17:40:00 +0200 Subject: [PATCH] Vorlesung 18 --- ...gik-logische-programmierung-einordnung.png | Bin 0 -> 237178 bytes Assets/Logik-prädikate-suche-fail-2.png | Bin 0 -> 97857 bytes Assets/Logik-prädikate-suche-fail.png | Bin 0 -> 106572 bytes Assets/Logik-prädikate-suche.png | Bin 0 -> 96785 bytes Logik und Logikprogrammierung.md | 137 ++++++++++++++++++ 5 files changed, 137 insertions(+) create mode 100644 Assets/Logik-logische-programmierung-einordnung.png create mode 100644 Assets/Logik-prädikate-suche-fail-2.png create mode 100644 Assets/Logik-prädikate-suche-fail.png create mode 100644 Assets/Logik-prädikate-suche.png diff --git a/Assets/Logik-logische-programmierung-einordnung.png b/Assets/Logik-logische-programmierung-einordnung.png new file mode 100644 index 0000000000000000000000000000000000000000..99fc2eaec40c709b4eda71b3b7646c4b22c64d47 GIT binary patch literal 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wahr ab, gdw. +- das Prädikat $chef_von(X,Y)$ das Paar $[X,Y]$ auf wahr abbildet oder +- es ein $Z\in I$ gibt, so dass + - das Prädikat $chef_von(X,Z)$ das Paar $[X,Z]$ auf wahr abbildet und + - das Prädikat $weisungsrecht(Z,Y)$ das Paar $[Z,Y]$ auf wahr abbildet. + +> Prozedurale Interpretation +Die Prozedur $weisungsrecht(X,Y)$ wird abgearbeitet, indem +1. die Unterprozedur $chef_von(X,Y)$ abgearbeitet wird. Im Erfolgsfall ist die Abarbeitung beendet; anderenfalls werden +2. die Unterprozeduren $chef_von(X,Z)$ und $weisungsrecht(Z,Y)$ abgearbeitet; indem systematisch Prozedurvarianten beider Unterprozeduren aufgerufen werden.Dies geschieht bis zum Erfolgsfall oder erfolgloser erschöpfender Suche. + + +| deklarative Interpretation | prozedurale Interpretation | +| --- | --- | +Prädikat | Prozedur +Ziel | Prozeduraufruf +Teilziel | Unterprozedur +Klauseln mit gleichem Kopfprädikat | Prozedur-varianten +Klauselkopf | Prozedurkopf +Klauselkörper | Prozedurrumpf + +Die Gratwanderung zwischen Wünschenswertem und technisch Machbarem erfordert mitunter „Prozedurales Mitdenken“, um +1. eine gewünschte Reihenfolge konstruktiver Lösungen zu erzwingen, +2. nicht terminierende (aber – deklarativ, d.h. logisch interpretiert - völlig korrekte) Programme zu vermeiden, +3. seiteneffektbehaftete Prädikate sinnvoll einzusetzen, +4. (laufzeit-) effizienter zu programmieren und +5. das Suchverfahren gezielt zu manipulieren. + +Programm inkl. Deklarationsteil (BSP3.PRO) +``` +domains + person = symbol +predicates + chef_von(person,person) + weisungsrecht(person,person) +clauses + chef_von(mueller,mayer). + chef_von(mayer,otto). + chef_von(otto,walter). + chef_von(walter,schulze). + weisungsrecht(X,Y) :- chef_von(X,Y). + weisungsrecht(X,Y) :- chef_von(X,Z), weisungsrecht(Z,Y). +goal + weisungsrecht(Wer,Wem). +``` + +Prädikate zur Steuerung der Suche nach einer Folge von Resolutionsschritten! + +!(cut) +Das Prädikat $!/0$ ist stets wahr. In Klauselkörpern eingefügt verhindert es ein Backtrack der hinter $!/0$ stehenden Teilziele zu den vor $!/0$ stehenden Teilzielen sowie zu alternativen Klauseln des gleichen Kopfprädikats. Die Verarbeitung von $!/0$ schneidet demnach alle vor der Verarbeitung verbliebenen Lösungswege betreffenden Prozedur ab. + +Prädikate zur Steuerung der Suche: $!/0$ +![](Assets/Logik-prädikate-suche.png) + + +Prädikate zur Steuerung der Suche nach einer Folge von Resolutionsschritten +**fail** +Das Prädikat $fail/0$ ist stets falsch. In Klauselkörpern eingefügt löst es ein Backtrack aus bzw. führt zum Misserfolg, falls der Backtrack-Keller leer ist, d.h. falls es keine verbleibenden Lösungswege (mehr) gibt. +![BSP4.PRO](Assets/Logik-prädikate-suche-fail.png) +![BSP4.PRO](Assets/Logik-prädikate-suche-fail-2.png) + +### Listen und rekursive Problemlösungsstrategien +Listen +1. $[]$ ist eine Liste. +2. Wenn $T$ ein Term und $L$ eine Liste ist, dann ist + 1. $[T|L]$ eine Liste. + 2. $T.L$ eine Liste. (ungebräuchlich) + 3. $.(T,L)$ eine Liste. (ungebräuchlich) + Das erste Element $T$ heißt Listenkopf, $L$ heißt Listenkörper oder Restliste. +3. Wenn $t_1, ... ,t_n$ Terme sind, so ist $[t_1,...,t_n]$ eine Liste. +4. Weitere Notationsformen von Listen gibt es nicht. + + + +Listen als kompakte Wissensrepräsentation: ein bekanntes Beispiel (BSP5.PRO) +- arbeiten_in([meier, mueller], raum_1). + - arbeitet_in(meier, raum_1). + - arbeitet_in(mueller, raum_1). +- arbeitet_in(otto, raum_2). + - arbeiten_in([otto], raum_2 ). +- arbeitet_in(kraus, raum_3). + - arbeiten_in([kraus], raum_3 ). +- anschluesse_in([raum_2, raum_3]). + - anschluss_in(raum_2). + - anschluss_in(raum_3). + +**Rekursion** in der Logischen Programmierung +Eine Prozedur heißt (direkt) rekursiv, wenn in mindestens einem der Klauselkörper ihrer Klauseln ein erneuter Aufruf des Kopfprädikates erfolgt. +Ist der Selbstaufruf die letzte Atomformel des Klauselkörpers der letzten Klausel dieser Prozedur - bzw. wird er es durch vorheriges „Abschneiden“ nachfolgender +Klauseln mit dem Prädikat $!/0$ - , so spricht man von Rechtsrekursion ; anderenfalls von Linksrekursion. +Eine Prozedur heißt indirekt rekursiv, wenn bei der Abarbeitung ihres Aufrufes ein erneuter Aufruf derselben Prozedur erfolgt. + +Wissensverarbeitung mit Listen: (BSP5.PRO) +- erreichbar(K) :- arbeitet_in(K,R), anschluss_in(R). + - erreichbar(K) :- anschluesse_in(Rs), member(R, Rs), arbeiten_in(Ks, R), member(K, Ks). +- koennen_daten_austauschen(K1,K2) :- arbeitet_in(K1,R),arbeitet_in(K2,R). + - koennen_daten_austauschen(K1,K2) :- arbeiten_in(Ks,_),member(K1,Ks), member(K2,Ks). +- koennen_daten_austauschen(K1,K2) :- erreichbar(K1),erreichbar(K2). + - koennen_daten_austauschen(K1,K2) :- erreichbar(K1),erreichbar(K2). + +BSP5.PRO +``` +domains + person, raum = symbol + raeume = raum* + personen = person* +predicates + arbeiten_in(personen, raum) + anschluesse_in(raeume) + erreichbar(person) + koennen_daten_austauschen(person,person) + member(person,personen) + member(raum,raeume) +clauses + ... (siehe oben) + member(E,[E|_]). + member(E,[_|R]) :- member(E,R). +goal + erreichbar(Wer). +``` + +**Unifikation 2er Listen** +1. Zwei leere Listen sind (als identische Konstanten aufzufassen und daher) miteinander unifizierbar. +1. Zwei nichtleere Listen $[K_1|R_1]$ und $[K_2|R_2]$ sind miteinander unifizierbar, wenn ihre Köpfe ($K_1$ und $K_2$) und ihre Restlisten ($R_1$ und $R_2$) jeweils miteinander unifizierbar sind. +3. Eine Liste $L$ und eine Variable $X$ sind miteinander unifizierbar, wenn die Variable selbst nicht in der Liste enthalten ist. Die Variable $X$ wird bei erfolgreicher Unifikation mit der Liste $L$ instanziert: $X:=L$. +