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Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)
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Cerutti--Knowledge Representation and Reasoning (postgrad seminar @ University of Brescia)

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  • 1. University of BresciaDepartment of Information EngineeringKnowledge Engineering and Human-Computer Interaction Research GroupKnowledge Representation andReasoning: an (extremely short)OverviewFederico CeruttiGestione dei Sistemi Informativi AziendaliFriday 1stJune, 2012c 2012 Federico Cerutti <federico.cerutti@ing.unibs.it>
  • 2. The Basic ConceptsKnowledge: some information about the world:medical information about some particular set of diseases: whatcauses them, how to diagnose them;geographical data: which city is the capital of which country,population statistics, . . . ;common sense physics: bodies cannot go through solid walls, . . .Representation: how/in which language do we represent thisinformation;Reasoning: how to extract more information from what isexplicitly represented (because we cannot represent every singlefact explicitly as in a database).c 2012 Federico Cerutti <federico.cerutti@ing.unibs.it> GSIA :: Friday 1st June, 2012 2
  • 3. The Basic ConceptsWe want to be able to talk about some AI programs in terms ofwhat they know;. . . and not just talk about what they know but also havesomething to point to in those systems corresponding toknowledge and determining their behaviour, namely explicitlyrepresented symbolic knowledge.c 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 2
  • 4. Why Knowledge Representation and Reasoning isSO ImportantExpert Systems:MYCYN (1970s, Stanford University)XCON (1978, Carnegie Mellon University)Ontologies:CYC (1980s-today Cycorp, Austin, Texas)WordNetSemantic Web applicationsReasoning about uncertainty:GoogleAmazonFacebook (ads)c 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 3
  • 5. KRR in Classical LogicKRR in Description LogicsKRR in Non-Monotonic LogicsConclusionsc 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 4
  • 6. Classical Logic: the First Order LogicA signature is a set of symbols of two kinds: function constantsand predicate constants with a non-negative integer called thearity assigned to each symbol: function constants of arity 0 arecalled object constants, while predicate constants of arity 0 arecalled propositional constants;Object variables are elements of some xed innite sequence ofsymbols (e.g. x, y, z, x1, x2, . . .);Terms of a signature σ are formed from object variables and fromfunction constants of σ;An atomic formula of σ is an expression of the form P(t1, . . . , tn)or t1 = t2 where P is a predicate constant of arity n and each ti isa term of σ;Formulas are formed from atomic formulas using propositionalconnectives ( , ⊥, ¬, ∧ or , ∨, → or ⊃, ↔ or ≡) and thequantiers ∃, ∀.c 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 5
  • 7. Variable ScopeLike variables in programming languages, the variables in FOL have ascope determined by the quantiers.P(x) ∧ ∃y[P(y) ∨ Q(y)]x is a free variable, y is a bound variableA closed formula, or a sentence, is a formula without freevariables;The universal closure of a formula F is the sentence ∀v1, . . . , vnF,where v1, . . . , vn are the free variables of F;The result of the substitution of a term t for a variable v in aformula F (or F[v/t]) is the formula obtained from F bysimultaneously replacing each free occurrence of v by t.c 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 6
  • 8. SemanticsAn interpretation or structure of a signature σ consists of:a nonempty set |I| called the universe (or domain) of I;for every object constant c of σ, an element cI of |I|;for every function constant f of σ of arity n 0, a function fIfrom |I|n to |I|;for every propositional constant P of σ, an element PI of{FALSE, TRUE};for every predicate constant R of σ of arity n 0, a function RIfrom |I|n to |I|.c 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 7
  • 9. SemanticsFor any element ξ of its universe |I|, select a new symbol ξ∗called the nameof ξ. By σIwe denote the signature obtained from σ adding all names ξ∗asobject constants. The interpretation I can be extended to the new signatureσIby dening (ξ∗)I= ξ for all ξ ∈ |I|.If t is an object constant, then tIis part of the interpretation I;For all function constants f of arity n 0,f(t1, . . . , tn)I= fI(tI1, . . . , tIn);For any propositional constant P, PIis part of the interpretation I,otherwise we dene:R(t1, . . . , tn) = RI(tI1, . . . , tIn),⊥I= FALSE, I= TRUE,(¬F)I= ¬(FI),(F G)I= (FI, GI) for every binary connective ,∀wF(w)I= TRUE if F(ξ∗)I= TRUE for all ξ ∈ |I|,∃wF(w)I= TRUE if F(ξ∗)I= TRUE for some ξ ∈ |I|.c 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 7
  • 10. SemanticsAn interpretation I satises a sentence F, or is a model of F(I F) if FI = TRUE;A sentence F is logically valid if every interpretation satises F;Two sentences are equivalent to each other if they are satised bythe same interpretations;A formula with free variables is said to be logically valid if itsuniversal closure is logically valid;Formulas F and G that may contain free variables are equivalentto each other if F ↔ F is logically valid;A set Γ of sentences is satisable if there exists an interpretationsatisfying all sentences in Γ;A set Γ of sentences entails a formula F (F F) if everyinterpretation satisfying Γ satises the universal closure of F.c 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 7
  • 11. Knowledge Representation and Reasoning withFOLExampleTony, Mike and John belong to the Alpine Club. Every member of theAlpine Club who is not a skier is a mountain climber. Mountain climbers donot like rain, and anyone who does not like snow is not a skier. Mike dislikeswhatever Tony likes, and likes whatever Tony dislikes. Tony likes rain andsnow.Prove that the given sentences logically entail that there is a member ofAlpine Club who is a mountain climber but not a skier.KB = {member(tony), member(cmike), member(john),∀ x (member(x) ∧ ¬skier(x)) → climber(x),∀ x climber(x) → ¬like(x, rain),∀ x ¬like(x, snow) → −skier(x),∀ x like(tony, x) → ¬like(mike, x),∀ x ¬like(tony, x) → like(mike, x),like(tony, rain), like(tony, snow)}c 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 8
  • 12. Knowledge Representation and Reasoning withFOLTo prove if KB ∃ x member(x) ∧ climber(x) ∧ ¬skier(x), let us considerthe Prover9 tool [McCune, 2010] fromhttp://www.cs.unm.edu/~mccune/prover9/.c 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 8
  • 13. Knowledge Representation and Reasoning withFOLc 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 8
  • 14. Knowledge Representation and Reasoning withFOLReduction ad absurdum.c 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 8
  • 15. KRR in Classical LogicKRR in Description LogicsKRR in Non-Monotonic LogicsConclusionsc 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 9
  • 16. Description LogicsFamily of logic-based knowledge representation formalisms well-suitedfor the representation of, and reasoning about:terminological knowledge;congurations;ontologies;database schemata:schema design, evolution, and query optimisationsource integration in heterogeneous databases/data warehousesconceptual modelling of multidimensional aggregation. . .. . .c 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 10
  • 17. DL SyntaxA description logic is mainly characterised by a set of constructorsthat allow to build complex:concepts correspond to classes (are interpreted as set of objects);roles correspond to relations (are interpreted as binary relationson objects).The DL ALC (Attributive concept Language with Complements):NC set of concept names, NR set of role names;, ⊥, and every concept name A ∈ NC is an ALC-conceptdescription;if C and D are ALC-concept descriptions, and r ∈ NR, thenC D, C D, ¬C, ∀r.C, ∃r.C are ALC-concept descriptions.c 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 11
  • 18. DL SyntaxExample (from [Horrocks and Sattler, 2002]).Man (∃has-child.Blue) (∃has-child.Green)(∀has-child.Happy Rich)c 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 11
  • 19. DL SemanticsSemantics given by means of an interpretation I = (∆I, ·I), with∆I = ∅ the domain of I, and ·I that maps every ALC-concept to asubset of ∆I, and every role name to a subset of ∆I × ∆I s.t.I = ∆I, ⊥I = ∅;(C D)I = CI ∩ DI;(C D)I = CI ∪ DI;(¬C)I = ∆I CI;(∃r.C)I = {x ∈ ∆I|∃y ∈ ∆I, x, y ∈ rI ∧ y ∈ CI};(∀r.C)I = {x ∈ ∆I|∀y ∈ ∆I, x, y ∈ rI → y ∈ CI};c 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 12
  • 20. DL Knowledge Bases: TBoxesThe TBox contains (Terminological Knowledge):Concept denitions, A.= C, where A is a concept name and C isa ALC-concept (e.g. Father.= Man ∃has-child.Human);Axioms, C1 C2, where Ci are ALC-concepts(∃favourite.Brewery ∃drinks.Beer).An interpretation I satises:a concept denition A.= C i AI = CI;an axiom C1 C2 i CI1 ⊆ CI2 ;a TBox T i I satises all denitions and axioms in T . In thiscase, I is a model of T (I T ).c 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 13
  • 21. DL Knowledge Bases: ABoxesThe ABox contains (Assertional knowledge):Concept assertions a : C, where a is an individual name, C aALC-concept (John : Man ∀has-child.(Male Happy));Role assertions a1, a2 : r, where ai are individual names, r is arole ( John, Bill : has-child)An interpretation I satises:a concept assertion a : C i aI ∈ CI;a role assertion a1, a2 : r i aI1 , aI2 ∈ rI;an ABox A i I satises all assertions in A. In this case, I is amodel of A (I A).c 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 14
  • 22. DL EntailmentEntailment in DL is dened as in FOL.A DL KB entails a concept c (KB c) i for every I, if I KB,then I c.c 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 15
  • 23. Semantic WebI have a dream for the Web [in which computers] becomecapable of analyzing all the data on the Web the content,links, and transactions between people and computers. ASemantic Web, which should make this possible, has yet toemerge, but when it does, the day-to-day mechanisms oftrade, bureaucracy and our daily lives will be handled bymachines talking to machines. The intelligent agents peoplehave touted for ages will nally materialize.[Berners-Lee and Fischetti, 2000]c 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 16
  • 24. Resource Description Framework (RDF): anexampleTitle Artist Country Company Price YearEmpire Burlesque Bob Dylan USA Columbia 10.90 1985Hide your heart Bonnie Tyler UK CBS Records 9.90 1988r d f : D e s c r i p t i o nrdf:about= http: //www. recshop . fake /cd/Empire Burlesque c d : a r t i s tBob Dylan/ c d : a r t i s tcd:countryUSA/ cd:countrycd:companyColumbia/cd:companyc d : p r i c e10.90/ c d : p r i c ecd:year1985/ cd:year/ r d f : D e s c r i p t i o nr d f : D e s c r i p t i o nrdf:about= http: //www. recshop . fake /cd/Hide your heart c d : a r t i s tBonnie Tyler/ c d : a r t i s tcd:countryUK/ cd:countrycd:companyCBS Records/cd:companyc d : p r i c e9.90/ c d : p r i c ecd:year1988/ cd:year/ r d f : D e s c r i p t i o nc 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 17
  • 25. Applications May Want MoreComplex applications may want more possibilities:characterisation of propertiesidentication of objects with dierent URIsdisjointness or equivalence of classesconstruct classes, not only name themmore complex classication schemesreason about some terms, e.g. if Person resources A and Bhave the same foaf:email property, then A and B areidentical. . .c 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 18
  • 26. OWL (Lite or DL)A semantic web ontology language developed by the W3C;Design goal: mapping from OWL to an expressive DL (exploitDL results);An OWL ontology can be seen to correspond to a DL TBoxtogether with a role hierarchy, describing the domain in terms ofclasses (corresponding to concepts) and properties (correspondingto roles).Human Maleo w l : C l a s so w l : i n t e r s e c t i o n O f r d f : p a r s e T y p e= C o l l e c t i o n o w l : C l a s s r d f : a b o u t=#Human/o w l : C l a s s r d f : a b o u t=#Male // o w l : i n t e r s e c t i o n O f/ o w l : C l a s sc 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 19
  • 27. OWL Constructors and Axioms (partial)Constructor DL syntaxinstersectionOf C1 · · · CnunionOF C1 · · · CncomplementOf ¬CallValuesFrom ∀P.CsomeValuesFrom ∃P.CAxiom DL syntaxsubClassOf C1 C2equivalentClass C1.= C2disjointWith C1 ¬C2c 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 20
  • 28. Protege Ontology EditorPeople ontology fromhttp://owl.man.ac.uk/2005/07/sssw/people.owlAn old lady is an eldery, female person, who has some animalsbut only cats.A cat is an animal.Minnie is an eldery female, and she has a pet, Tom.Who has a pet, is a person.Since Minnie has a pet, she is a person.Since Minnie is an eldery, female person, she is a old lady.Since Minnie is an old lady, and she has a pet, Tom, and since oldladies have only cats, Tom is a cat.c 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 21
  • 29. DL and Other FormalismsMost DLs are decidable fragments of FOL (ALC-concepts can bemapped into rst order formulae);DLs far more expressive than ALC:number restrictions: people having at most 2 cats and exactly 1dogcomplex roles:inverse (has-child, child-of);transitive closure (offspring, has-child);role inclusion (has-daughter, has-child);. . .c 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 22
  • 30. A More Expressive Logic: the Second-Order LogicRicher syntax than FOL because, along with object variables, weassume now an innite sequence of function variables of arity n 0,and an innite sequence of predicate variables of arity n ≥ 0. Objectvariables are viewed as function variables of arity 0.∀α, β ∃γ ∀x (γ(x) = α(β(x)))Sentence expressing the possibility of composing any two functions∀x, y (Q(x, y) ↔ ∀q (F(q) → q(x, y)))where F(q) stands for∀x1, y1 (P(x1, y1) → q(x1, y1))∧∀x1, y1, z1 ((q(x1, y1) ∧ q(y1, z1)) → q(x1, z1))Q is the intersection of all transitive relations containing Pc 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 23
  • 31. CycThe Cyc Knowledge Server is a very large knowledge base andinference engineDeveloped by Cycorp http://www.cyc.com/It aims to provide a deep layer of common sense knowledge tobe used by other knowledge-intensive programsContains terms and assertions in formal language CycL, basedsecond order logicKnowledge base contains classication of things, facts, rules ofthumb, heuristics for reasoning about everyday objects.c 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 24
  • 32. Cyc Example of Opposite Relationshipsc r e a t e c o n s t a n t k1c r e a t e c o n s t a n t k2(# $ i s a #$k1 #$ S c a l a r I n t e r v a l )(# $ i s a #$k2 #$ S c a l a r I n t e r v a l )(#$muchLessThan #$k1 #$k2 )Query : (#$muchGreaterThan ?X ?Y)c 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 25
  • 33. KRR in Classical LogicKRR in Description LogicsKRR in Non-MonotonicLogicsConclusionsc 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 26
  • 34. Non Monotonic LogicsClassical logic is monotonic: whenever a sentence A is a logicalconsequence of a set of sentences T (T A), then A is also aconsequence of an arbitrary superset of T;Commonsense reasoning is dierent: we often draw plausibleconclusions based on the assumption that the world is normaland as expected;This is farm from being irrational: it is the best we can do insituations in which we have only incomplete information;It can happen that our normality assumptions turn out to bewrong: in this case we may have to revise our conclusions.c 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 27
  • 35. The Tweety ExampleBirds ies, in Prolog: assert((flies(X) :- bird(X))).c 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 28
  • 36. The Tweety ExampleBirds ies, in Prolog: assert((flies(X) :- bird(X))).Tweety is a bird. . . (assert(bird(tweety)).)c 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 28
  • 37. The Tweety ExampleBirds ies, in Prolog: assert((flies(X) :- bird(X))).Tweety is a bird. . . (assert(bird(tweety)).). . . then Tweety ies.c 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 28
  • 38. The Tweety ExampleBirds ies, in Prolog: assert((flies(X) :- bird(X))).Tweety is a bird. . . (assert(bird(tweety)).). . . then Tweety ies.Tux is a penguin (penguin(tux).)c 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 28
  • 39. The Tweety ExampleBirds ies, in Prolog: assert((flies(X) :- bird(X))).Tweety is a bird. . . (assert(bird(tweety)).). . . then Tweety ies.Tux is a penguin (penguin(tux).)Every penguin is a bird (bird(X) :- penguin(X).)c 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 28
  • 40. The Tweety ExampleBirds ies, in Prolog: assert((flies(X) :- bird(X))).Tweety is a bird. . . (assert(bird(tweety)).). . . then Tweety ies.Tux is a penguin (penguin(tux).)Every penguin is a bird (bird(X) :- penguin(X).)Then Tux ies (?!?!)c 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 28
  • 41. The Tweety Example RevisitedBirds ies unless they are abnormal(flies(X) :- bird(X), + abnormalbird(X).)+ means negation as failure, equivalent to:not(P) :- call(P), !, fail. if P, then not(P) failsnot(P). else not(P) holdsc 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 29
  • 42. The Tweety Example RevisitedBirds ies unless they are abnormal(flies(X) :- bird(X), + abnormalbird(X).)+ means negation as failure, equivalent to:not(P) :- call(P), !, fail. if P, then not(P) failsnot(P). else not(P) holdsWe know that penguin are abnormal birds(abnormalbird(X) :- penguin(X). andbird(X) :- penguin(X).)c 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 29
  • 43. The Tweety Example RevisitedBirds ies unless they are abnormal(flies(X) :- bird(X), + abnormalbird(X).)+ means negation as failure, equivalent to:not(P) :- call(P), !, fail. if P, then not(P) failsnot(P). else not(P) holdsWe know that penguin are abnormal birds(abnormalbird(X) :- penguin(X). andbird(X) :- penguin(X).)Tweety is a bird (we do not know if normal or abnormal). . . (bird(tweety).)c 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 29
  • 44. The Tweety Example RevisitedBirds ies unless they are abnormal(flies(X) :- bird(X), + abnormalbird(X).)+ means negation as failure, equivalent to:not(P) :- call(P), !, fail. if P, then not(P) failsnot(P). else not(P) holdsWe know that penguin are abnormal birds(abnormalbird(X) :- penguin(X). andbird(X) :- penguin(X).)Tweety is a bird (we do not know if normal or abnormal). . . (bird(tweety).)Tux is a penguin. . . (penguin(tux).)c 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 29
  • 45. The Tweety Example RevisitedBirds ies unless they are abnormal(flies(X) :- bird(X), + abnormalbird(X).)+ means negation as failure, equivalent to:not(P) :- call(P), !, fail. if P, then not(P) failsnot(P). else not(P) holdsWe know that penguin are abnormal birds(abnormalbird(X) :- penguin(X). andbird(X) :- penguin(X).)Tweety is a bird (we do not know if normal or abnormal). . . (bird(tweety).)Tux is a penguin. . . (penguin(tux).). . . Tweety ies, Tux does not.c 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 29
  • 46. The Tweety Example RevisitedBirds ies unless they are abnormal(flies(X) :- bird(X), + abnormalbird(X).)+ means negation as failure, equivalent to:not(P) :- call(P), !, fail. if P, then not(P) failsnot(P). else not(P) holdsWe know that penguin are abnormal birds(abnormalbird(X) :- penguin(X). andbird(X) :- penguin(X).)Tweety is a bird (we do not know if normal or abnormal). . . (bird(tweety).)Tux is a penguin. . . (penguin(tux).). . . Tweety ies, Tux does not.What would happen if we know that also Tweety is a penguin?(penguin(tweety).)c 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 29
  • 47. The Tweety Example RevisitedBirds ies unless they are abnormal(flies(X) :- bird(X), + abnormalbird(X).)+ means negation as failure, equivalent to:not(P) :- call(P), !, fail. if P, then not(P) failsnot(P). else not(P) holdsWe know that penguin are abnormal birds(abnormalbird(X) :- penguin(X). andbird(X) :- penguin(X).)Tweety is a bird (we do not know if normal or abnormal). . . (bird(tweety).)Tux is a penguin. . . (penguin(tux).). . . Tweety ies, Tux does not.What would happen if we know that also Tweety is a penguin?(penguin(tweety).)Tweety does not y.c 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 29
  • 48. A Logic for Default Reasoning (sketched)[Reiter, 1980]A default theory is a pair (D, W) where W is a set of sentences inrst order logic, and D is a set of defaults.A default is an expression:A : B1, . . . , BnCRecalling Tweety example:Bird(x) : MFly(x)Fly(x)MFly it is consistent to assume that ies∀x, Penguin(x) → ¬Fly(x)c 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 30
  • 49. Answer Set ProgrammingAnswer Set Programming is a recent problem solving approach;It has roots in KR, logic programming, and nonmonotonicreasoning;The idea: stop trying to prove something, represent solutions, ormodels (Answer Sets)!Normal logic program P is a nite set of rules of the form:a ← b1, . . . , bm, not c1, . . . , not cnwhere a, bi, cj are literals of the form p or ¬p (strong negation,also written as -) where p is a rst-order atom from a classicalFOL signature.An answer set is a set of ground atoms that are collectivelyacceptablec 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 31
  • 50. Answer Set Programming: the Tweety Examplef l i e s (X) :− b i r d (X) , not abnormal (X ) .abnormal (X) :− penguin (X ) .b i r d (X) :− penguin (X ) .b i r d ( tweety ) .penguin ( tux ) .Resulting Answer Sets:{ penguin ( tux ) , f l i e s ( tweety ) , b i r d ( tweety ) ,b i r d ( tux ) , abnormal ( tux ) }c 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 32
  • 51. Answer Set Programming: the Nixon DiamondUsually, Quakers are pacistUsually, Republicans are not pacistRichard Nixon is both a Quaker and a Republicanquaker ( nixon ) .r e p u b l i c a n ( nixon ) .p a c i f i s t (X) :− quaker (X) , not −p a c i f i s t (X ) .−p a c i f i s t (X) :− r e p u b l i c a n (X) , not p a c i f i s t (X ) .Resulting Answer Sets:{ quaker ( nixon ) , r e p u b l i c a n ( nixon ) , p a c i f i s t ( nixon ) }{ quaker ( nixon ) , r e p u b l i c a n ( nixon ) , −p a c i f i s t ( nixon ) }c 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 33
  • 52. Argumentation: an Informal Example (Courtesyof Prof. Massimiliano Giacomin)The reasonThe conclusionWe are justified in believing that we should run LHC We should run Large Hadron ColliderLHC allows us tounderstand the Lawsof the UniverseUnderstandingthe Laws of theUniverse is goodc 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 34
  • 53. Argumentation: an Informal Example (Courtesyof Prof. Massimiliano Giacomin)The reasonThe conclusionWe are justified in believing that we should run LHC We should run Large Hadron ColliderLHC allows us tounderstand the Lawsof the UniverseUnderstandingthe Laws of theUniverse is goodIn Argumentation (and in real life as well):- reasons are not necessary “conclusive”(they don’t logically entail conclusions)- arguments and conclusions can be “retracted”in front of new information, i.e. counterargumentsBUTc 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 34
  • 54. Argumentation: an Informal Example (Courtesyof Prof. Massimiliano Giacomin)We should run Large Hadron ColliderLHC allows us tounderstand the Lawsof the UniverseUnderstandingthe Laws of theUniverse is goodWe should not run LHCLHC will generateblack holesdestroying EarthDestroyingEarthis badNow we are justified in believing that we should not run LHC c 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 34
  • 55. Argumentation: an Informal Example (Courtesyof Prof. Massimiliano Giacomin)We should run Large Hadron ColliderLHC allows us tounderstand the Lawsof the UniverseUnderstandingthe Laws of theUniverse is goodWe should not run LHCLHC will generateblack holesdestroying EarthDestroyingEarthis badBlack holes willnot destroy EarthBlack holes willevaporate becauseof Hawking radiationNow we are again justified in believing that we should run LHC c 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 34
  • 56. Argumentation: an Informal Example (Courtesyof Prof. Massimiliano Giacomin)We should run Large Hadron ColliderLHC allows us tounderstand the Lawsof the UniverseUnderstandingthe Laws of theUniverse is goodWe should not run LHCLHC will generateblack holesdestroying EarthDestroyingEarthis badBlack holes willnot destroy EarthBlack holes willevaporate becauseof Hawking radiationHawking radiationdoes not existDr Azzeccagarbuglisays soNow we are again justified in believing that we should not run LHC c 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 34
  • 57. Argumentation: an Informal Example (Courtesyof Prof. Massimiliano Giacomin)We should run Large Hadron ColliderLHC allows us tounderstand the Lawsof the UniverseUnderstandingthe Laws of theUniverse is goodWe should not run LHCLHC will generateblack holesdestroying EarthDestroyingEarthis badBlack holes willnot destroy EarthBlack holes willevaporate becauseof Hawking radiationHawking radiationdoes not existDr Azzeccagarbuglisays soDr Azzeccagarbugliis not expert in physicsHe is a lawyerNow we are again justifiedin believing that we shouldrun LHC c 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 34
  • 58. What is Argumentation?[Prakken, 2011] Argumentation is the process of supportingclaims with grounds and defending them against attack.[van Eemeren et al., 1996] Argumentation is a verbal and socialactivity of reason aimed at increasing (or decreasing) theacceptability of a controversial standpoint for the listener orreader, by putting forward a constellation of propositionsintended to justify (or refute) the standpoint before a rationaljudge.A framework for practical and uncertain reasoning able to copewith partial and inconsistent knowledge.c 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 35
  • 59. The Elements of an Argumentation System[Prakken and Vreeswijk, 2001]1 The denition of an argument (possibly including an underlyinglogical language + a notion of logical consequence)2 The notion of attack and defeat (successful attack) betweenarguments;3 An argumentation semantics selecting acceptable (justied)argumentsc 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 36
  • 60. Arguments and Attacks: Assumption-BasedArgumentation [Bondarenko et al., 1993]An Assumption-Based Argumentation (ABA) system is a tupleL, R, A,¯· s.t.L is a set of sentences;R is a set of rules of the form s1 ← s2, . . . sn where each si is asentence;A ⊆ L is a set of candidate assumptions, and each assumptioncannot be the head of any rule;¯a is the contrary of assumption a;An argument is a deduction supported by a set of assumptions;An argument A attacks another argument A if the conclusion ofA is the contrary of one of the assumptions supporting A .c 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 37
  • 61. Arguments and Attacks: ABA Example (from[Gaertner and Toni, 2008])Assumptions: {all_likes(adrian), mom_hates(adrian)}Rules:{acceptable(adrian) ←all_like(adrian), easy_to_remember(adrian)easy_to_remember(adrian) ← short(adrian)some_dislike(adrian) ← mom_hates(adrian)some_dislike(adrian) ← dad_hates(adrian)dad_hates(adrian) ← too_common(adrian)dad_hates(adrian) ← uncle_has(adrian)mom_not_hate(adrian) ← mom_said_ok(adrian)mom_said_ok(adrian)short(adrian)}Contraries: all_like(adrian) = some_dislike(adrian),mom_hates(adrian) = mom_not_hate(adrian).c 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 38
  • 62. Arguments and Attacks: Argument Schemes[Walton, 1996]An argument scheme is a reasoning pattern giving us thepresumption in favour of its conclusion.A critical question is a question that can be posed by an opponentin order to undermine the validity of the stated argument.There are several argument schemes in literature.Expert testimonyPremise 1: E is expert on DPremise 2: E says PPremise 3: P is in DConclusion: P is the caseCritical questions:1 Is E biased?2 Is P consistent with what other experts say?3 Is P consistent with known evidence?c 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 39
  • 63. Argumentation Semantics: AbstractArgumentation [Dung, 1995]1 The denition of an argument (possibly including an underlyinglogical language + a notion of logical consequence)2 The notion of attack and defeat (successful attack) betweenarguments;3 An argumentation semantics selecting acceptable (justied)argumentsAbstract argumentation focuses on the third aspect.An abstract argumentation framework AF is a tuple A, R , where Ais a set of argument (whose origin and structure is not specied), andR ⊆ A × A is a set of attack (or defeat) relations.Argument evaluation: given an argumentation framework, determinethe justication state (defeat status) of arguments. In particular, whatargument emerge undefeated from the conict, i.e. are acceptable?c 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 40
  • 64. Nixon DiamondAFN = AN , RN , where AN = {A1, A2}, RN = { A1, A2 , A2, A1 },andA1: since Nixon is a quaker, then he is also a pacist;A2: since Nixon is a republican, he is not a pacist.c 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 41
  • 65. Argumentation Semantics (Courtesy of Prof.Massimiliano Giacomin)• Specification of a method for argument evaluation, or ofcriteria to determine, given a set of arguments, their “defeat status”Argumentation FrameworkSemanticsDefeat statusDefeat statusUndefeatedDefeatedProvisionally Defeatedc 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 42
  • 66. Extension-based Semantics (Courtesy of Prof.Massimiliano Giacomin)Set of extensions ℰS(AF)Argumentation framework AFSemantics SDefeat/Justification StatusSkeptically justied argument: belongs to all the extensions;Credulously justied argument: belongs to at least one;Indefensible argument: does not belong to any extension.c 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 43
  • 67. Complete Semantics (Courtesy of Prof.Massimiliano Giacomin)Acceptabilityα acceptable w.r.t. (“defended by”) S• all attackers of α are attacked by SAdmissible set S• conflict-free• every element acceptable w.r.t. S(defends all of its elements)αSIFalso includes allacceptable elementsw.r.t. itselfCompleteextensionComplete semanticsAll traditional semanticsselect complete extensionsc 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 44
  • 68. Complete Semantics Examples (Courtesy of Prof.Massimiliano Giacomin)α β γChainAdmissible sets:ø, {α}, {α, γ}Only one complete extension:ℰCO(AF) = {{α, γ}}Nixon DiamondβαβαβαβαAll admissible setsare completeℰCO(AF) ={ ø, {α}, {β} }c 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 45
  • 69. Complete Semantics Examples (Courtesy of Prof.Massimiliano Giacomin)Nixon Diamond + nodeβαβαβαAdmissible sets:ø, {α}, {β}, {α, γ}ℰCO(AF) = {ø{α, γ},{β} }βα γℰCO(AF)γγγc 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 45
  • 70. Grounded Semantics (Courtesy of Prof.Massimiliano Giacomin)UndefeatedDefeatedProvisionally DefeatedGrounded extension GE(AF):Least complete extensionDefeat statusincluded in all extensionsof any traditional semanticsGrounded semantics isthe “most skeptical” onec 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 46
  • 71. Grounded Semantics Examples (Courtesy of Prof.Massimiliano Giacomin)α β γChainGE(AF) = {α, γ}Nixon Diamondβα GE(AF) = øNixon Diamond + nodeβα γ GE(AF) = øc 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 47
  • 72. Grounded Semantics Problem (Courtesy of Prof.Massimiliano Giacomin)βαγ δβαγ δ VSWhat we (may) wantGrounded Semantics• Actually, grounded semantics is polynomially computable• But sometimes a more discriminative behavior is desirableTHE CASE OF FLOATING ARGUMENTS• A problem for all possible unique status approachesLet us consider multiple status approaches!c 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 48
  • 73. Preferred Semantics (Courtesy of Prof.Massimiliano Giacomin)Preferred semanticsPreferred extensionMaximal complete extension = max Set:• is conflict-free• defends all of its elements[P.M. Dung, ’95]Stable extensions are maximal complete extensions• conflict-free: by definition• admissible: every argument attacking an extension is outside⇒ attacked by the extension itself• maximal: no argument can be included!c 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 49
  • 74. Preferred Semantics Examples (Courtesy of Prof.Massimiliano Giacomin)βαγ δβαγ δβαγ δβαγ δβαγ δGrounded semantics:ℰPR(AF) = ℰST(AF) = { {α, δ}, {β, δ} } ⇒ δ is justifiedc 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 50
  • 75. KRR in Classical LogicKRR in Description LogicsKRR in Non-Monotonic LogicsConclusionsc 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 51
  • 76. ConclusionsKnowledge: some information about the world;Representation: how to represent this information:Classical Logic;Description Logics;Nonmonotonic Logics;Reasoning: how to extract more information from what isexplicitly represented:logic inference;representing solutions (or models).c 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 52
  • 77. What is Not Covered in This Presentation(among the others)SAT Solver;CSP;Conceptual Graphs;Autoepistemic Reasoning;Belief revision;Modal logic;Deontic logic;Temporal reasonnig;Spatial reasoning;Physical reasoning;Event calculus;Temporal action logic;Multi-agent systems;Bayesian Networks;Neural Networks;Markovian Chains;. . .c 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 53
  • 78. Suggested Readingsc 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 54
  • 79. Suggested Readingsc 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 54
  • 80. Suggested Readingsc 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 54
  • 81. Suggested Readingsc 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 54
  • 82. Suggested Readingsc 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 54
  • 83. Suggested Readingsc 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 54
  • 84. Suggested Readingsc 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 54
  • 85. References I[Alechina, 2011] Alechina, N. (2011).Knowledge representation and reasoning 2011-2012: G53KRR course slides.http://www.cs.nott.ac.uk/~nza/G53KRR/.[Berners-Lee and Fischetti, 2000] Berners-Lee, T. and Fischetti, M. (2000).Weaving the Web.HarperBusiness.[Bondarenko et al., 1993] Bondarenko, A., Toni, F., and Kowalski, R. (1993).An assumption-based framework for non-monotonic reasoning.In Nerode, A. and Pereira, L., editors, Proceedings Second International Workshop on LogicProgramming and Non-Monotonic Reasoning. MIT Press.[Brachman and Levesque, 2004a] Brachman, R. and Levesque, H. (2004a).Knowledge Representation and Reasoning.Elsevier.[Brachman and Levesque, 2004b] Brachman, R. and Levesque, H. (2004b).Knowledge representation and reasoning: Overhead slides.http://www.cs.toronto.edu/~hector/PublicKRSlides.pdf.[Dung, 1995] Dung, P. M. (1995).On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logicprogramming, and n-person games.Articial Intelligence, 77(2):321357.c 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 55
  • 86. References II[Gaertner and Toni, 2008] Gaertner, D. and Toni, F. (2008).Hybrid argumentation and its properties.In Proceedings of COMMA 2008.[Herman, 2011] Herman, I. (2011).Introduction to the semantic web.http://www.w3.org/2011/Talks/0606-SemTech-Tut-IH/Talk.pdf.[Horrocks and Sattler, 2002] Horrocks, I. and Sattler, U. (2002).Description logics - basics, applications, and more (tutorial at ecai-2002).http://www.cs.man.ac.uk/~horrocks/Slides/ecai-handout.pdf.[McCune, 2010] McCune, W. (20052010).Prover9 and mace4.http://www.cs.unm.edu/~mccune/prover9/.[Prakken, 2011] Prakken, H. (2011).An overview of formal models of argumentation and their application in philosophy.Studies in Logic, 4:6586.[Prakken and Vreeswijk, 2001] Prakken, H. and Vreeswijk, G. A. W. (2001).Logics for defeasible argumentation.In Gabbay, D. M. and Guenthner, F., editors, Handbook of Philosophical Logic, Second Edition.Kluwer Academic Publishers, Dordrecht.c 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 56
  • 87. References III[Reiter, 1980] Reiter, R. (1980).A logic for default reasoning.Articial Intelligence, 13(1-2):81 132.[van Eemeren et al., 1996] van Eemeren, F. H., Grootendorst, R., Johnson, R. H., Plantin, C., Walton,D. N., Willard, C. A., Woods, J., and Zarefsky, D. (1996).Fundamentals of Argumentation Theory. A Handbook of Historical Backgrounds andContemporary Developments.Lawrence Erlbaum Associates.[van Harmelen et al., 2007] van Harmelen, F., van Harmelen, F., Lifschitz, V., and Porter, B. (2007).Handbook of Knowledge Representation.Elsevier Science, San Diego, USA.[W3C, 2012] W3C (2012).Rdf tutorial.http://www.w3schools.com/rdf/default.asp.[Walton, 1996] Walton, D. N. (1996).Argumentation Schemes for Presumptive Reasoning.Lawrence Erlbaum Associates.c 2012 Federico Cerutti federico.cerutti@ing.unibs.it GSIA :: Friday 1st June, 2012 57

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