Ontology-based Interpretation of Natural Language II - Resolution-based theorem proving dwigand | ggoetze | semeyerz Resolution-based theorem proving Otter.

Präsentation zum Thema: "Ontology-based Interpretation of Natural Language II - Resolution-based theorem proving dwigand | ggoetze | semeyerz Resolution-based theorem proving Otter."—  Präsentation transkript:

1 Ontology-based Interpretation of Natural Language II - Resolution-based theorem proving dwigand | ggoetze | semeyerz Resolution-based theorem proving Otter / Prover9 Dennis Leroy Wigand | Gereon Goetze | Sebastian Meyer zu Borgsen

2 Ontology-based Interpretation of Natural Language II - Resolution-based theorem proving dwigand | ggoetze | semeyerz Aufgabenstellung Vorstellung von Prover9 Basis Aufgaben: Father and Son ToBI the Robot Enlighted Room Problematik der Modellierung von zeitlichen Abläufen Neue Prover9 Version Production Mode Highlighting und Aufbau einer Input-Datei Zeitontology Aufgaben Manuel Neuer Ronaldo Gomez Variante 1 Ronaldo Gomez Variante 2 Resümee Agenda

3 Ontology-based Interpretation of Natural Language II - Resolution-based theorem proving dwigand | ggoetze | semeyerz Einarbeiten ins Theorem Proving für First-order logics: Verwendung von Otter/Prover9 Implementierung kleiner Bsp. John is the son of Peter. Entwicklung einer Ontologie für zeitliche Abläufe. Erweiterung der Ontologie auf den Spezialfall Fussball. Aufgabenstellung …ein kurzer Überblick

4 Ontology-based Interpretation of Natural Language II - Resolution-based theorem proving dwigand | ggoetze | semeyerz Theorembeweiser für Prädikatenlogik erster Stufe (von William McCune). Nachfolger vom OTTER (Organized Techniques Theorem proving and effective Research) Theorem Prover. Unterscheidet nicht mehr zwischen Klauseln und Formeln. Versucht im Gegensatz zu Mace4 einen Beweis zu finden. (Prover9 Beweis, Mace4 Gegenbeispiel) Prover9

5 Ontology-based Interpretation of Natural Language II - Resolution-based theorem proving dwigand | ggoetze | semeyerz Resolution – Aufgabe I Aufbau Father and Son John is the son of Peter. Resolution von John is male. AussageKonsistentInformativ John is male. John is female.

6 Ontology-based Interpretation of Natural Language II - Resolution-based theorem proving dwigand | ggoetze | semeyerz Resolution – Aufgabe I Proof Father and Son

7 Ontology-based Interpretation of Natural Language II - Resolution-based theorem proving dwigand | ggoetze | semeyerz Resolution – Aufgabe II Aufbau ToBI the Robot All robots enjoy life. ToBI is a robot. AussageKonsistentInformativ ToBI enjoys life. There is someone who does not enjoy life. formulas(usable). % Relations % All robots enjoy life. all x (Robot(x) -> enjoysLife(x)). end_of_list. formulas(assumptions). % Knowledge % ToBI is a robot. Robot(ToBI). end_of_list. formulas(goals). % Goals % ToBI enjoys life. enjoysLife(ToBI). % There is someone % who does not enjoy life. exists x (-enjoysLife(x)). end_of_list.

8 Ontology-based Interpretation of Natural Language II - Resolution-based theorem proving dwigand | ggoetze | semeyerz Resolution – Aufgabe III Aufbau Enlighted Room John entered the room. The electricity was not off. Either the electricity was off or he switched on the light. AussageKonsistentInformativ John switched on the light. The room was not dark anymore. % Either the electricity was off or he switched on the light. -(entered(y,x) & electricityOff(x)) switchOnLight(y,x). switchOnLight(y,x) -> -dark(x).% Relation for not dark question. entered(John,Room).% John entered the room. -electricityOff(Room).% The electricity was not off. switchOnLight(John,Room).% John switched on the light. % -dark(Room).% The room was not dark anymore.

9 Ontology-based Interpretation of Natural Language II - Resolution-based theorem proving dwigand | ggoetze | semeyerz Problematik der Modellierung …First-order Logic und ihre Tücken Spielminuten 90 Spielminuten Ordnung über die Zeit Punktestände Vergleichbarkeit (2 Tore > 1) Ergebnis von Toren Semantische Interpretation des gegebenen Satzes early header … canceled out

10 Ontology-based Interpretation of Natural Language II - Resolution-based theorem proving dwigand | ggoetze | semeyerz Versionswechsel …und der Weg zu neuen Möglichkeiten Grafische Oberfläche von Prover9 nutzt LADR-Dec-2007 Aktuelle Version LADR-Dec-2009-11A keine graphische Oberfläche nur als Source Code verfügbar Production Mode

11 Ontology-based Interpretation of Natural Language II - Resolution-based theorem proving dwigand | ggoetze | semeyerz Highlighting …optimales Arbeiten auch ohne GUI Erstellung eines Highlightings für Prover9/Mace4 Dateien (*.in)

12 Ontology-based Interpretation of Natural Language II - Resolution-based theorem proving dwigand | ggoetze | semeyerz Prover9 Input Datei …Aufbau der einzelnen Sektionen

13 Ontology-based Interpretation of Natural Language II - Resolution-based theorem proving dwigand | ggoetze | semeyerz Production Mode …randvoll mit mächtigen Features Ermöglicht die Nutzung von Zahlen (1,2,3..) Operatoren (+/- ) Ordnung auf Zahlen Listen ([y:z]) Rekursion Variablen (u,v,w,x,y,z)

14 Ontology-based Interpretation of Natural Language II - Resolution-based theorem proving dwigand | ggoetze | semeyerz Manuel Neuer Aufbau Aufgabenstellung Manuel Neuer is the goalkeeper of Bayern München. AussageKonsistentInformativ He plays for Schalke. He played for Schalke. Dazu bedarf es… …einer Zeitontology für die Modellierung der zeitlichen Einordnung von Events.

15 Ontology-based Interpretation of Natural Language II - Resolution-based theorem proving dwigand | ggoetze | semeyerz Manuel Neuer Aufbau Zeitontology % Enables the use of numbers and arithmetics. set(production). formulas(usable).% Relations ----------------------------------------- % Interval u before interval v. all u all v (before(u,v) <- Interval(u,x,y) & Interval(v,z,w) & (y <= z) & -equal(u,v)). % Inequality of intervals. Interval(u,x,y) & Interval(v,z,w) & (-(x == z)|-(y == w)) -> -equal(u,v). % Instant v in Interval u. instDuringInt(v,u) = y) & (x <= z). % Checks for overlapping intervals. overlaps(v,u) <- Interval(v,x,y) & Interval(u,w,z) & ((x >= w) & (x = w) & (y <= z)).

16 Ontology-based Interpretation of Natural Language II - Resolution-based theorem proving dwigand | ggoetze | semeyerz Manuel Neuer Aufbau Inhalt % A goalkeeper is a player (now). goalkeeper(x,y) -> player(x,y). % Past events can be attached to a specific time. wasGoalkeeper(x,y,z) -> playedFor(x,y,z). % Get the corresponding interval to the "now"-instant. player(x,y) & instDuringInt(now,z) -> playedFor(x,y,z). % Rule out that a player cannot play for two different clubs at the same time (overlapping intervals). all b (Interval(b,v,w) & playedFor(x,y,z) & -(y == u) & overlaps(z,b) -> -playedFor(x,u,b)). % Wrapper for playedFor with corresponding interval to the "now"-instant. playedFor(x,y,z) & instDuringInt(now,z) -> playsFor(x,y). -playedFor(x,y,z) & instDuringInt(now,z) -> -playsFor(x,y).

17 Ontology-based Interpretation of Natural Language II - Resolution-based theorem proving dwigand | ggoetze | semeyerz Manuel Neuer Aufbau Goals % Manuel Neuer plays for Schalke. playsFor(ManuelNeuer,Schalke). % Manuel Neuer played for Schalke. % (Find an interval, % which is before the "now"-interval.) exists x exists y (before(x,y) & instDuringInt(now,y) & playedFor(ManuelNeuer,Schalke,x)). KonsistentInformativ

18 Ontology-based Interpretation of Natural Language II - Resolution-based theorem proving dwigand | ggoetze | semeyerz Ronaldo Gomez Aufbau Aufgabenstellung The 90 th minute header by Gomez cancelled out the early opener by Ronaldo AussageKonsistentInformativ ??? Hier gibt es verschiedene Ansätze… …zwei davon werden im Folgenden vorgestellt - jeweils mit Pro/Contra.

19 Ontology-based Interpretation of Natural Language II - Resolution-based theorem proving dwigand | ggoetze | semeyerz Vorteile der Versionen

20 Ontology-based Interpretation of Natural Language II - Resolution-based theorem proving dwigand | ggoetze | semeyerz Demo Live Demos

21 Ontology-based Interpretation of Natural Language II - Resolution-based theorem proving dwigand | ggoetze | semeyerz Resümee …die Quintessenz zum Schluss Grenzen der FOL. Problematik der Ambiguität von Sprache. Selbstverständlichkeit von Numerik. Überführen von Open- in Closed-World.