Knowledge Representation Knowledge Representation Plan for today Knowledge-based systems 1 Explicit knowledge Knowledge Representation Inferred knowledge Domain-specific stuff A very brief intro Changing premises Uncertainty Jacek Malec Semantic anchoring Dept. of Computer Science, Lund University Architectures 2 February 20, 2019 Self-awareness 3 Jacek Malec, Computer Science, Lund University 1(29) Jacek Malec, Computer Science, Lund University 2(29) Knowledge Representation Knowledge Representation Explicit knowledge Explicit knowledge Facts about: Facts about: objects Jacek Malec, Computer Science, Lund University 3(29) Jacek Malec, Computer Science, Lund University 3(29)
Knowledge Representation Knowledge Representation Explicit knowledge Explicit knowledge Facts about: Facts about: objects objects places places times Jacek Malec, Computer Science, Lund University 3(29) Jacek Malec, Computer Science, Lund University 3(29) Knowledge Representation Knowledge Representation Explicit knowledge Explicit knowledge Facts about: Facts about: objects objects places places times times events events processes processes behaviours behaviours vehicle dynamics rigid body interactions traffic laws . . . Jacek Malec, Computer Science, Lund University 3(29) Jacek Malec, Computer Science, Lund University 3(29)
Knowledge Representation Knowledge Representation Explicit knowledge Explicit knowledge Background knowledge for all this includes: Background knowledge for all this includes: ontologies Jacek Malec, Computer Science, Lund University 4(29) Jacek Malec, Computer Science, Lund University 4(29) Knowledge Representation Knowledge Representation Explicit knowledge Explicit knowledge Background knowledge for all this includes: Background knowledge for all this includes: ontologies ontologies theories theories physics mereology . . . Jacek Malec, Computer Science, Lund University 4(29) Jacek Malec, Computer Science, Lund University 4(29)
Knowledge Representation Knowledge Representation Explicit knowledge Inferred knowledge Background knowledge for all this includes: ontologies (or: turning implicit into explicit) theories logics (language) 1 physics theorem proving (mechanics) 2 mereology modes of reasoning 3 . . . Not everything needs to be explicit, nor expressed in one monolithic formalism Jacek Malec, Computer Science, Lund University 4(29) Jacek Malec, Computer Science, Lund University 5(29) Knowledge Representation Knowledge Representation Logics: modal Logics: modal take a logical language, let α be a wff take a logical language, let α be a wff 1 1 ⇤ α is a wff ⇤ α is a wff 2 2 ⌃ α is a wff ⌃ α is a wff 3 3 normally ⇤ α $ ¬ ⌃ ¬ α normally ⇤ α $ ¬ ⌃ ¬ α 4 4 Intended meaning? Intended meaning? ⇤ α means Necessarily α 1 Jacek Malec, Computer Science, Lund University 6(29) Jacek Malec, Computer Science, Lund University 6(29)
Knowledge Representation Knowledge Representation Logics: modal Logics: modal take a logical language, let α be a wff take a logical language, let α be a wff 1 1 ⇤ α is a wff ⇤ α is a wff 2 2 ⌃ α is a wff ⌃ α is a wff 3 3 normally ⇤ α $ ¬ ⌃ ¬ α normally ⇤ α $ ¬ ⌃ ¬ α 4 4 Intended meaning? Intended meaning? ⇤ α means Necessarily α ⇤ α means Necessarily α 1 1 ⇤ α means Agent knows α ⇤ α means Agent knows α 2 2 ⇤ α means Agent believes α 3 Jacek Malec, Computer Science, Lund University 6(29) Jacek Malec, Computer Science, Lund University 6(29) Knowledge Representation Knowledge Representation Logics: modal Logics: modal take a logical language, let α be a wff take a logical language, let α be a wff 1 1 ⇤ α is a wff ⇤ α is a wff 2 2 ⌃ α is a wff ⌃ α is a wff 3 3 normally ⇤ α $ ¬ ⌃ ¬ α normally ⇤ α $ ¬ ⌃ ¬ α 4 4 Intended meaning? Intended meaning? ⇤ α means Necessarily α ⇤ α means Necessarily α 1 1 ⇤ α means Agent knows α ⇤ α means Agent knows α 2 2 ⇤ α means Agent believes α ⇤ α means Agent believes α 3 3 ⇤ α means Always in the future α ⇤ α means Always in the future α 4 4 G α means Always in the future (or: Globally) α 5 Jacek Malec, Computer Science, Lund University 6(29) Jacek Malec, Computer Science, Lund University 6(29)
Knowledge Representation Knowledge Representation Logics: Kripke semantics Logics: temporal Globally (always): 1 Actually, meaning of modal formulae is defined on graph structures ⇤ Φ Nodes: possible worlds Finally (eventually): 2 ⌃ Φ Edges: reachability relation Next: 3 � Φ ~p,q,~r p,q,~r ~p,q,r Until: 4 Ψ U Φ p,q,r p,q,~r ~p,~q,r p,q,r p,~q,r Jacek Malec, Computer Science, Lund University 7(29) Jacek Malec, Computer Science, Lund University 8(29) Knowledge Representation Knowledge Representation Logics: temporal Logics: description Earlier known as semantic networks. Formal version of semantic Globally (always): 1 web languages (OIL, DAML, OWL). ⇤ Φ Finally (eventually): 2 ⌃ Φ Next: 3 � Φ Until: 4 Ψ U Φ Effective reasoning: inheritance via SubsetOf (SubClass) and MemberOf (isA) links Cf. Richard Murray’s verification of autonomous car controller: intersection paths special meaning of some links (e.g. cardinality constraints) ( Φ e init ^ ⇤ Φ e safe ^ ⇤⌃ Φ e prog ) ! ( Φ s init ^ ⇤ Φ s safe ^ ⇤⌃ Φ s prog ) classification, consistency, subsumption Jacek Malec, Computer Science, Lund University 8(29) Jacek Malec, Computer Science, Lund University 9(29)
Knowledge Representation Knowledge Representation Representation: ontologies Modes of reasoning: Deduction RedLightAt ( intersection 1 ) 8 ( x ) RedLightAt ( x ) ! � StopBefore ( x ) thus � StopBefore ( intersection 1 ) General Pattern: prior facts 1 Lots of robot-related ontologies: domain knowledge 2 knowrob, IEEE CORA (Standard 1872-2015), intelligent systems observations 3 ontology (2005, NIST), ... Jacek Malec, Computer Science, Lund University 10(29) Jacek Malec, Computer Science, Lund University 11(29) Knowledge Representation Knowledge Representation Modes of reasoning: Deduction Modes of reasoning: Deduction RedLightAt ( intersection 1 ) RedLightAt ( intersection 1 ) 8 ( x ) RedLightAt ( x ) ! � StopBefore ( x ) 8 ( x ) RedLightAt ( x ) ! � StopBefore ( x ) thus thus � StopBefore ( intersection 1 ) � StopBefore ( intersection 1 ) General Pattern: General Pattern: prior facts prior facts 1 1 domain knowledge domain knowledge 2 2 observations observations 3 3 conclusions conclusions 4 4 Sound. Sound. But note: Birds fly. Tweety is a penguin. Penguins are birds. Jacek Malec, Computer Science, Lund University 11(29) Jacek Malec, Computer Science, Lund University 11(29)
Knowledge Representation Knowledge Representation Modes of reasoning: Induction Modes of reasoning: Abduction OnDesk ( monitor 1 ) ^ Monitor ( monitor 1 ) , General pattern: OnDesk ( monitor 2 ) ^ Monitor ( monitor 2 ) , prior facts 1 OnDesk ( monitor 3 ) ^ Monitor ( monitor 3 ) , domain knowledge OnDesk ( monitor 4 ) ^ Monitor ( monitor 4 ) , 2 OnDesk ( monitor 5 ) ^ Monitor ( monitor 5 ) observations 3 thus 8 ( x ) Monitor ( x ) ! OnDesk ( x ) General pattern: Observe 1 Generalize 2 Fallible. Constructs hypotheses, not true facts. However, most of our practical reasoning, in particular learning, is of this kind. Jacek Malec, Computer Science, Lund University 12(29) Jacek Malec, Computer Science, Lund University 13(29) Knowledge Representation Knowledge Representation Modes of reasoning: Abduction What do we want to represent? General pattern: objects prior facts 1 places domain knowledge 2 times observations 3 events explain the observation 4 processes Given a theory T and observations O behaviours E is an explanation of O given T if vehicle dynamics E [ T | = O and E [ T is consistent. rigid body interactions Usually we are interested in most plausible E , sometimes minimal E , most elegant E , ... traffic laws . . . Probablilistic abduction: maybe Elin will (or has) mention(ed) it. Jacek Malec, Computer Science, Lund University 13(29) Jacek Malec, Computer Science, Lund University 14(29)
Knowledge Representation Knowledge Representation Qualitative spatial reasoning Qualitative spatial reasoning Jacek Malec, Computer Science, Lund University 15(29) Jacek Malec, Computer Science, Lund University 16(29) Knowledge Representation Knowledge Representation Qualitative spatial reasoning Juggling example (Apt) RCC8: region connection calculus Given e.g., contains ( A , B ) ^ covers ( B , C ) we can conclude contains ( A , C ) ⇤ ( meet ( A , B ) ! � ( meet ( A , B ) _ disjoint ( A , B ) _ overlap ( A , B ))) Jacek Malec, Computer Science, Lund University 17(29) Jacek Malec, Computer Science, Lund University 18(29)
Knowledge Representation Knowledge Representation Interval calculus (Allen 1983) Invalidating conclusions Tweety is a bird. So it flies. Jacek Malec, Computer Science, Lund University 19(29) Jacek Malec, Computer Science, Lund University 20(29) Knowledge Representation Knowledge Representation Invalidating conclusions Invalidating conclusions Tweety is a bird. Tweety is a bird. So it flies. So it flies. But Tweety is a penguin. But Tweety is a penguin. So it doesn’t fly. So it doesn’t fly. Non-monotonic reasoning. Truth-maintenance systems. Default reasoning. Circumscription. Closed World Assumption. Negation as failure. . . . Jacek Malec, Computer Science, Lund University 20(29) Jacek Malec, Computer Science, Lund University 20(29)
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