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S  N)) XV_  \*=    N)) X1_   ^*=    NЩ)) X5G_  ^*=  H  0k\ ? www3PP80___PPT10.|2pw Default DesignB 0 aBYB 6`A(  ?"   `p0?QG  SComplexity of Contextual Reasoning Bounded Model Property for Multi-Context Systems2Tx#O16 8  QG ' QGA"   `0? [ ;Student: Floris Roelofsen University of Twente, NetherlandsD<x,,"  7"   `0?5 QG 1Advisor: Luciano Serafini ITC-IRST, Trento, ItalyD2x,,  C"    `P 0? ). +Occasion: ESSLLI Nancy, France, August 2004V,x ,,  J"    pAffff20?S" `?QG dAnalysis2 x,  "    f)0?"` R Problem of generality (McCarthy, 1987) Principle of locality (Giunchiglia, 1993)hS        "    `L#0?"`-  8 PLC: Prop. Logic of Context MCS: Multi-Context Systems 99  H"  s p=Affff20?S" `?~NQGq^ h Related Work2 x ,  E"    ?Affff20?S" `?jQG86 _Multi-Context Systems x, "   fP0?).& B x   zA  . pȜ9?panorama2agents%-%"   fR0?"` ( Intuition Multiple partial, approximate, and perspective representations& (Benerecetti et.al., 2000) & subject to certain compatibility constraints: if Mr. 1 sees a ball, then Mr. 2 also sees a ball.N   3 ."   fe0?"` /E( Example Contexts: I = {1,2} Languages: L1 = L({ l, r }) and L2 = L({ l, c, r }) Bridge rules: 1 : l v r ! 2 : l v c v r \{     O "   fģ0?"`)V C4 2Syntax A set of indices I, each of which denotes a context. Each context i T I is described by a formal language Li. Local expressions ~ labeled formulas: i :  Relational expressions ~ bridge rules: i :  ,& , i :  ! i :  A multi context system [ { Li }i TI ,BR] consists of a set of languages { Li }i TI and a set of bridge rules BR.7 !''&MU. #2  "   fxn0?"`)*EE4 $Semantics A chain c = { ci }i T I is a collection of sets of local models. A chain c satisfies an i  labeled formula  if all local models in ci (classically) satisfy . A chain complies with a bridge rule if it satisfies its consequence or does not satisfy one of its premises. A chain c is j  consistent if cj is nonempty. I   )  ,nY4 V"   Affff20?S" `?v7#GAM pBounded Model Property0x,  SL '<.BE  # :V 8D"   `0?"`'<.BE 6Contextual Satisfiability Problem Given a set of formulas  (addressing a set of contexts J ) and a set of bridge rules BR. Is there a chain, which: satisfies  complies with BR is J  consistent."s2" 8' OJ:Y % "   `h0?S"`?=A @eD U?*X "   f0?"`HEV J NBounded Model Property A set of formulas is contextually satisfiable iff it is satisfied by a chain which contains at most |J | + |BR| local models.~ eO  " !  fPS0?"`:%EJ X Proof Take any J  consistent chain c that satisfies  and complies with BR. For every j TJ, there must be at least one local model mj T cj that satisfies all j  labeled formulas in . Let BR* be the set of bridge rules whose consequences aren t satisfied by c. Every br T BR* must have a premise which is not satisfied by at least one local model mbr in c. Remove from c all models but: Uj TJ mj U Ubr T BR mbr. The resulting chain contextually satisfies  and contains at most |J | + |BR| local models.".  $ *Z NID6$+3WO&.2 F" ( s dAffff20?S" `?~N#q^ f Implications0 x ,  " 1  `D!0?"`TQV P\ F NP completeness for MCS. New complexity bounds: O (||2) for PLC (previously O (||4)) O ((|J| + |BR|) . N) for MCS (no previous result) (N is the total size of the formulas in  and BR) Tractable encoding of contextual satisfiability into purely propositional satisfiability.Z2^5_2-5_  J7dh@" 2  `\0?"`TQ*EP\  Contextual Decision Procedures. (Serafini & Roelofsen, KR 2004) (Roelofsen & Serafini & Cimatti, ECAI 2004) Reasoning in Distributed Description Logics. (Serafini & Tamilin, DL 2004) Partition based Reasoning. (Amir & McIlraith, KR 2000 / AIJ to appear)`!R.!/ D" 3 s \Affff20?S" `?\& d Motivation0 x ,  " 4 Z0?"`/E  * MCS more general than PLC (Serafini & Bouquet, AIJ 2004) NP completeness for PLC (Massacci, 1996)4"*g  =" 6 S ~lAffff0?S" `?w6 i Formalization2x ,  H  0k\ ? 3380___PPT10.|2wr0-&Rw(NKtaJ / 00DAriallar0TT$,ܖ 0ܖ"DCenturyr0TT$,ܖ 0ܖ DVerdanar0TT$,ܖ 0ܖ"0DCastellar0TT$,ܖ 0ܖ COh+'0,W `hx  Slide 1 roelofsen roelofsen25Microsoft Office PowerPoint@a@cy|2@;G(V   +(    """)))UUUMMMBBB999|PP3f333f3333f3ffffff3f̙3ff333f333333333f33333333f33f3ff3f3f3f3333f33̙33333f333333f3333f3ffffff3f33ff3f3f3f3fff3ffffffffff3ffff̙fff3fffff3fff333f3f3ff3ff33f̙̙3̙ff̙̙̙3f̙3f333f3333f3ffffff3f̙3f3f3f333f3333f3ffffff3f̙3f3ffffffffff!___www4(A |(|Mʦ 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roelofsenroelofsen    [CustomITCIG ArialCenturyVerdana CastellarDefault DesignSlide 1  Fonts UsedDesign Template Slide Titlesd@  @@``  7#7,b$< 7 v;wK 0AA@3ʚ;ʚ;g4!d!d8 0 p0p%<4dddd w 0T+ 80___PPT10 ppB 0 eB]B 6`A(  ?"   ``0?QG  SComplexity of Contextual Reasoning Bounded Model Property for Multi-Context Systems2Tx#O16  8  QG ' QGA"   `0? [ ;Student: Floris Roelofsen University of Twente, NetherlandsD<x,,"  7"   `0?5 QG 1Advisor: Luciano Serafini ITC-IRST, Trento, ItalyD2x,,  9"    ` 0? ). 3KR, Doctoral Consortium Whistler, Canada, June 2004D4x,  J"    Affff20?S" `?QG dAnalysis2 x,  "    f\ 0?"` R Problem of generality (McCarthy, 1987) Principle of locality (Giunchiglia, 1993)hS        "    `,0?"`-  8 PLC: Prop. Logic of Context MCS: Multi-Context Systems 99  H"  s =Affff20?S" `?~NQGq^ h Related Work2 x ,  E"    ?Affff20?S" `?jQG86 _Multi-Context Systems x, "   fP0?).& B x   zA  . pȜ9?panorama2agents%-%"   fR0?"` ( Intuition Multiple partial, approximate, and perspective representations& (Benerecetti et.al., 2000) & subject to certain compatibility constraints: if Mr. 1 sees a ball, then Mr. 2 also sees a ball.N   3 ."   f e0?"` /E( Example Contexts: I = {1,2} Languages: L1 = L({ l, r }) and L2 = L({ l, c, r }) Bridge rules: 1 : l v r ! 2 : l v c v r \{     O "   f0?"`)V C4 2Syntax A set of indices I, each of which denotes a context. Each context i T I is described by a formal language Li. Local expressions ~ labeled formulas: i :  Relational expressions ~ bridge rules: i :  ,& , i :  ! i :  A multi context system [ { Li }i TI ,BR] consists of a set of languages { Li }i TI and a set of bridge rules BR.7 !''&MU. #2  "   f  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~   ; !"#$%&'()*+,-./012345678<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{}~Root EntrydO)@;:@PictureswKCurrent User;SummaryInformation(\WPowerPoint Document( sDocumentSummaryInformation8O.   @n?" dd@  @@``  7#7,b$< 7 v;wK 0AA@3ʚ;ʚ;g4!d!d8 0 Vp0p%<4dddd w 0T, 80___PPT10 ppB 0 WBOB 6`A(  ?"   `p0?QG  SComplexity of Contextual Reasoning Bounded Model Property for Multi-Context Systems2Tx#O16  8  QG ' QGA"   `0? [ ;Student: Floris Roelofsen University of Twente, NetherlandsD<x,,"  7"   `0?5 QG 1Advisor: Luciano Serafini ITC-IRST, Trento, ItalyD2x,,  9"    `P 0? ). 3KR, Doctoral Consortium Whistler, Canada, June 2004D4x,  J"    pAffff20?S" `?QG dAnalysis2 x,  "    f)0?"` R Problem of generality (McCarthy, 1987) Principle of locality (Giunchiglia, 1993)hS        "    `L#0?"`-  8 PLC: Prop. Logic of Context MCS: Multi-Context Systems 99  H"  s p=Affff20?S" `?~NQGq^ h Related Work2 x ,  E"    ?Affff20?S" `?jQG86 _Multi-Context Systems x, "   fP0?).& B x   zA  . pȜ9?panorama2agents%-%"   fR0?"` ( Intuition Multiple partial, approximate, and perspective representations& (Benerecetti et.al., 2000) & subject to certain compatibility constraints: if Mr. 1 sees a ball, then Mr. 2 also sees a ball.N   3 ."   fe0?"` /E( Example Contexts: I = {1,2} Languages: L1 = L({ l, r }) and L2 = L({ l, c, r }) Bridge rules: 1 : l v r ! 2 : l v c v r \{     O "   fģ0?"`)V C4 2Syntax A set of indices I, each of which denotes a context. Each context i T I is described by a formal language Li. Local expressions ~ labeled formulas: i :  Relational expressions ~ bridge rules: i :  ,& , i :  ! i :  A multi context system [ { Li }i TI ,BR] consists of a set of languages { Li }i TI and a set of bridge rules BR.7 !''&MU. #2  "   fxn0?"`)*EE4 $Semantics A chain c = { ci }i T I is a collection of sets of local models. A chain c satisfies an i  labeled formula  if all local models in ci (classically) satisfy . A chain complies with a bridge rule if it satisfies its consequence or does not satisfy one of its premises. A chain c is j  consistent if cj is nonempty. I   )  ,nY4 V"   Affff20?S" `?v7#GAM pBounded Model Property0x,  SL '<.BE  # :V 8D"   `0?"`'<.BE 6Contextual Satisfiability Problem Given a set of formulas  (addressing a set of contexts J ) and a set of bridge rules BR. Is there a chain, which: satisfies  complies with BR is J  consistent."s2" 8' OJ:Y % "   `h0?S"`?=A @eD U?*X "   f0?"`HEV J NBounded Model Property A set of formulas is contextually satisfiable iff it is satisfied by a chain which contains at most |J | + |BR| local models.~ eO  " !  fPS0?"`:%EJ X Proof Take any J  consistent chain c that satisfies  and complies with BR. For every j TJ, there must be at least one local model mj T cj that satisfies all j  labeled formulas in . Let BR* be the set of bridge rules whose consequences aren t satisfied by c. Every br T BR* must have a premise which is not satisfied by at least one local model mbr in c. Remove from c all models but: Uj TJ mj U Ubr T BR mbr. The resulting chain contextually satisfies  and contains at most |J | + |BR| local models.".  $ *Z NID6$+3WO&.2 F" ( s dAffff20?S" `?~N#q^ f Implications0 x ,  " 1  `D!0?"`TQV P\ F NP completeness for MCS. New complexity bounds: O (||2) for PLC (previously O (||4)) O ((|J| + |BR|) . N) for MCS (no previous result) (N is the total size of the formulas in  and BR) Tractable encoding of contextual satisfiability into purely propositional satisfiability.Z2^5_2-5_  J7dh@" 2  `\0?"`TQ*EP\  Contextual Decision Procedures. (Serafini & Roelofsen, KR 2004) (Roelofsen & Serafini & Cimatti, ECAI 2004) Reasoning in Distributed Description Logics. (Serafini & Tamilin, DL 2004) Partition based Reasoning. (Amir & McIlraith, KR 2000 / AIJ to appear)`!R.!/ D" 3 s \Affff20?S" `?\& d Motivation0 x ,  " 4 Z0?"`/E  * MCS more general than PLC (Serafini & Bouquet, AIJ 2004) NP completeness for PLC (Massacci, 1996)4"*g  =" 6 S ~lAffff0?S" `?w6 i Formalization2x ,  H  0k\ ? 3380___PPT10.|2wrbRV>Rw(NKtaJ / 00DAriallar0TT,ܖ 0ܖDCenturyr0TT,ܖ 0ܖ DVerdanar0TT,ܖ 0ܖ"0DCastellar0TT,ܖ 0ܖ CO.   @n?" d՜.+,0    [CustomITC sMG ArialCenturyVerdana CastellarDefault DesignSlide 1  Fonts UsedDesign Template Slide Titles0?"`)*EE4 $Semantics A chain c = { ci }i T I is a collection of sets of local models. A chain c satisfies an i  labeled formula  if all local models in ci (classically) satisfy . A chain complies with a bridge rule if it satisfies its consequence or does not satisfy one of its premises. A chain c is j  consistent if cj is nonempty. I   )  ,nY4 V"   8nAffff20?S" `?v7#GAM pBounded Model Property0x,  SL '<.BE  # :V 8D"   `0?"`'<.BE 6Contextual Satisfiability Problem Given a set of formulas  (addressing a set of contexts J ) and a set of bridge rules BR. Is there a chain, which: satisfies  complies with BR is J  consistent."s2" 8' OJ:Y % "   `0?S"`?=A @eD U?*X "   fp0?"`HEV J NBounded Model Property A set of formulas is contextually satisfiable iff it is satisfied by a chain which contains at most |J | + |BR| local models.~ eO  " !  f|S0?"`:%EJ X Proof Take any J  consistent chain c that satisfies  and complies with BR. For every j TJ, there must be at least one local model mj T cj that satisfies all j  labeled formulas in . Let BR* be the set of bridge rules whose consequences aren t satisfied by c. Every br T BR* must have a premise which is not satisfied by at least one local model mbr in c. Remove from c all models but: Uj TJ mj U Ubr T BR mbr. The resulting chain contextually satisfies  and contains at most |J | + |BR| local models.".  $ *Z NID6$+3WO&.2 F" ( s Affff20?S" `?~N#q^ f Implications0 x ,  " 1  `/0?"`TQV P\ F NP completeness for MCS. New complexity bounds: O (||2) for PLC (previously O (||4)) O ((|J| + |BR|) . N) for MCS (no previous result) (N is the total size of the formulas in  and BR) Tractable encoding of contextual satisfiability into purely propositional satisfiability.Z2^5_2-5_  J7dh>" 2  `0?"`TQ*EP\  Contextual Decision Procedures. (Serafini & Roelofsen, KR 2004) (Roelofsen, Serafini & Cimatti, ECAI 2004) Reasoning in Distributed Description Logics. (Serafini & Tamilin, DL 2004) Partition based Reasoning. (Amir & McIlraith, KR 2000 / AIJ to appear)`!Q.!/ D" 3 s Affff20?S" `?\& d Motivation0 x ,  " 4 Z0?"`/E  : MCS more general than PLC (Serafini & Bouquet, AIJ 2004) NP completeness for PLC (Massacci, AAAI 1996)4"2o  =" 6 S ~Affff0?S" `?w6 i Formalization2x ,  H  0k\ ? 3380___PPT10.|2wrw(NKtaJ / 00DAriallar0TT,ܖ 0ܖ"DCenturyr0TT,ܖ 0ܖ DVerdanar0TT,ܖ 0ܖ"0DCastellar0TT,ܖ 0ܖ CO.   @n?" dd@  @@``  7"7,b$< 7 v;wK 0AA@3ʚ;ʚ;g4 d d8 0Lp0p%<4dddd w 0T+ 80___PPT10 qqC 0 7C/C 6pB(  ?"   ``0?QG  SComplexity of Contextual Reasoning Bounded Model Property for Multi-Context Systems2Tx#O16 ?"   f0? z ;Student: Floris Roelofsen University of Twente, NetherlandsD<x,,"  5"   f0? 3QG 1Advisor: Luciano Serafini ITC-IRST, Trento, ItalyD2x,,  7"    f 0? . 3KR, Doctoral Consortium Whistler, Canada, June 2004D4x,  J"    Affff20?S" `?QG dAnalysis2 x,  "    f\ 0?"`z X Problem of generality (McCarthy, 1987) Principle of locality (Giunchiglia, 1993)   #    "    `,0?"`I0  x PLC: Propositional Logic of Context (McCarthy, Guha, Buva , et. al.) MCS: Multi-Context Systems (Giunchiglia, Serafini, et. al.)>%$$  H"  s =Affff20?S" `?~NQGq^ h Related Work2 x ,  E"    ?Affff20?S" `?jQG86 _Multi-Context Systems x, "   fP0?.& B x   zA  . pȜ9?panorama2agents%-%"   fR0?"` ( Intuition Multiple partial, approximate, and perspective representations& (Benerecetti et.al., 2000) & subject to certain compatibility constraints: if Mr. 1 sees a ball, then Mr. 2 also sees a ball.N   3 ."   f e0?"` I0E( Example Contexts: I = {1,2} Languages: L1 = L({ l, r }) and L2 = L({ l, c, r }) Bridge rules: 1 : l v r ! 2 : l v c v r \{     O "   f0?"`)V C4 2Syntax A set of indices I, each of which denotes a context. Each context i T I is described by a formal language Li. Local expressions ~ labeled formulas: i :  Relational expressions ~ bridge rules: i :  ,& , i :  ! i :  A multi context system [ { Li }i TI ,BR] consists of a set of languages { Li }i TI and a set of bridge rules BR.7 !''&MU. #2  "   f0?"`)*EE4 $Semantics A chain c = { ci }i T I is a collection of sets of local models. A chain c satisfies an i  labeled formula  if all local models in ci (classically) satisfy . A chain complies with a bridge rule if it satisfies its consequence or does not satisfy one of its premises. A chain c is j  consistent if cj is nonempty. I   )  ,nY4 V"   8nAffff20?S" `?v7#GAM pBounded Model Property0x,  SL '<.BE  # :V 8D"   `0?"`'<.BE 6Contextual Satisfiability Problem Given a set of formulas  (addressing a set of contexts J ) and a set of bridge rules BR. Is there a chain, which: satisfies  complies with BR is J  consistent."s2" 8' OJ:Y % "   `0?S"`?=A @eD U?*X "   fp0?"`HEV J NBounded Model Property A set of formulas is contextually satisfiable iff it is satisfied by a chain which contains at most |J | + |BR| local models.~ eO  " !  f|S0?"`:%EJ X Proof Take any J  consistent chain c that satisfies  and complies with BR. For every j TJ, there must be at least one local model mj T cj that satisfies all j  labeled formulas in . Let BR* be the set of bridge rules whose consequences aren t satisfied by c. Every br T BR* must have a premise which is not satisfied by at least one local model mbr in c. Remove from c all models but: Uj TJ mj U Ubr T BR mbr. The resulting chain contextually satisfies  and contains at most |J | + |BR| local models.".  $ *Z NID6$+3WO&.2 F" ( s Affff20?S" `?~N#q^ f Implications0 x ,  " 1  `/0?"`TQV P\ F NP completeness for MCS. New complexity bounds: O (||2) for PLC (previously O (||4)) O ((|J| + |BR|) . N) for MCS (no previous result) (N is the total size of the formulas in  and BR) Tractable encoding of contextual satisfiability into purely propositional satisfiability.Z2^5_2-5_  J7dh>" 2  `0?"`TQ*EP\  Contextual Decision Procedures. (Serafini & Roelofsen, KR 2004) (Roelofsen, Serafini & Cimatti, ECAI 2004) Reasoning in Distributed Description Logics. (Serafini & Tamilin, DL 2004) Partition based Reasoning. (Amir & McIlraith, KR 2000 / AIJ to appear)`!Q.!/ D" 3 s Affff20?S" `?\& d Motivation0 x ,  " 4 Z0?"`3E  : MCS more general than PLC (Serafini & Bouquet, AIJ 2004) NP completeness for PLC (Massacci, AAAI 1996)4"2o  =" 6 S ~Affff0?S" `?w6 i Formalization2x ,  H  0k\ ? 3380___PPT10.|2wryH*w(NKtaJ / 00DAriallar0TT,ܖ 0ܖ"DCenturyr0TT,ܖ 0ܖ DVerdanar0TT,ܖ 0ܖ"0DCastellar0TT,ܖ 0ܖ CO.   @n?" dd@  @@``  7"7,b$< 7 v;wK 0AA@3ʚ;ʚ;g4dd8 0 p0p%<4dddd w 0T+ 80___PPT10 qqC 0 7C/C 6pB(  ?"   ``0?QG  SComplexity of Contextual Reasoning Bounded Model Property for Multi-Context Systems2Tx#O16 ?"   f0? z ;Student: Floris Roelofsen University of Twente, NetherlandsD<x,,"  5"   f0? 3QG 1Advisor: Luciano Serafini ITC-IRST, Trento, ItalyD2x,,  7"    f 0? . 3KR, Doctoral Consortium Whistler, Canada, June 2004D4x,  J"    Affff20?S" `?QG dAnalysis2 x,  "    f\ 0?"`z X Problem of generality (McCarthy, 1987) Principle of locality (Giunchiglia, 1993)   #    "    `,0?"`I0  x PLC: Propositional Logic of Context (McCarthy, Guha, Buva , et. al.) MCS: Multi-Context Systems (Giunchiglia, Serafini, et. al.)>%$$  H"  s =Affff20?S" `?~NQGq^ h Related Work2 x ,  E"    ?Affff20?S" `?jQG86 _Multi-Context Systems x, "   fP0?.& B x   zA  . pȜ9?panorama2agents%-%"   fR0?"` ( Intuition Multiple partial, approximate, and perspective representations& (Benerecetti et.al., 2000) & subject to certain compatibility constraints: if Mr. 1 sees a ball, then Mr. 2 also sees a ball.N   3 ."   f e0?"` I0E( Example Contexts: I = {1,2} Languages: L1 = L({ l, r }) and L2 = L({ l, c, r }) Bridge rules: 1 : l v r ! 2 : l v c v r \{     O "   f0?"`)V C4 2Syntax A set of indices I, each of which denotes a context. Each context i T I is described by a formal language Li. Local expressions ~ labeled formulas: i :  Relational expressions ~ bridge rules: i :  ,& , i :  ! i :  A multi context system [ { Li }i TI ,BR] consists of a set of languages { Li }i TI and a set of bridge rules BR.7 !''&MU. #2  "   f0?"`)*EE4 $Semantics A chain c = { ci }i T I is a collection of sets of local models. A chain c satisfies an i  labeled formula  if all local models in ci (classically) satisfy . A chain complies with a bridge rule if it satisfies its consequence or does not satisfy one of its premises. A chain c is j  consistent if cj is nonempty. I   )  ,nY4 V"   8nAffff20?S" `?v7#GAM pBounded Model Property0x,  SL '<.BE  # :V 8D"   `0?"`'<.BE 6Contextual Satisfiability Problem Given a set of formulas  (addressing a set of contexts J ) and a set of bridge rules BR. Is there a chain, which: satisfies  complies with BR is J  consistent."s2" 8' OJ:Y % "   `0?S"`?=A @eD U?*X "   fp0?"`HEV J NBounded Model Property A set of formulas is contextually satisfiable iff it is satisfied by a chain which contains at most |J | + |BR| local models.~ eO  " !  f|S0?"`:#EJ X Proof Take any J  consistent chain c that satisfies  and complies with BR. For every j TJ, there must be at least one local model mj T cj that satisfies all j  labeled formulas in . Let BR* be the set of bridge rules whose consequences aren t satisfied by c. Every br T BR* must have a premise which is not satisfied by at least one local model mbr in c. Remove from c all models but: Uj TJ mj U Ubr T BR mbr. The resulting chain contextually satisfies  and contains at most |J | + |BR| local models.".  $ *Z NID6$+3WO&.2 F" ( s Affff20?S" `?~N#q^ f Implications0 x ,  " 1  `/0?"`TQV P\ F NP completeness for MCS. New complexity bounds: O (||2) for PLC (previously O (||4)) O ((|J| + |BR|) . N) for MCS (no previous result) (N is the total size of the formulas in  and BR) Tractable encoding of contextual satisfiability into purely propositional satisfiability.Z2^5_2-5_  J7dh>" 2  `0?"`TQ*EP\  Contextual Decision Procedures. (Serafini & Roelofsen, KR 2004) (Roelofsen, Serafini & Cimatti, ECAI 2004) Reasoning in Distributed Description Logics. (Serafini & Tamilin, DL 2004) Partition based Reasoning. (Amir & McIlraith, KR 2000 / AIJ to appear)`!Q.!/ D" 3 s Affff20?S" `?\& d Motivation0 x ,  " 4 Z0?"`3E  : MCS more general than PLC (Serafini & Bouquet, AIJ 2004) NP completeness for PLC (Massacci, AAAI 1996)4"2o  =" 6 S ~Affff0?S" `?w6 i Formalization2x ,  H  0k\ ? 3380___PPT10.|2wr*/`*rwRoot EntrydO)z1<PictureswKCurrent User;SummaryInformation(\W   ; !"#$%&'()*+,-./012345678<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{}~ PowerPoint Document( sDocumentSummaryInformation84՜.+,D՜.+,    [CustomITC sMG ArialCenturyVerdana CastellarDefault DesignSlide 1  Fonts UsedDesign Template Slide Titles!_r roelofsenroelofsen4 $,    [CustomITCIG ArialCenturyVerdana CastellarDefault DesignSlide 1  Fonts UsedDesign Template Slide Titles