Time Representation of Events Pascal Amsili Introduction (1) a. - PowerPoint PPT Presentation

The Negation Time Representation of Events Pascal Amsili Introduction (1) a. Jones loves a woman. Davidson b. ∃ x woman( x ) ∧ love( j , x ) Initial Problem 1 Initial Problem 2 Reification Discussion Parsons Kamp&Reyle The question Observations and arguments Complete Proposal Conclusion & Perspectives References 4 / 40

The Negation Time Representation of Events Pascal Amsili Introduction (1) a. Jones loves a woman. Davidson b. ∃ x woman( x ) ∧ love( j , x ) Initial Problem 1 Initial Problem 2 Reification Discussion would equally represent Parsons Kamp&Reyle The question (2) a. Jones loved a woman. Observations and arguments b. Jones will love a woman. Complete Proposal Conclusion & Perspectives References 4 / 40

The Negation Time Representation of Events Pascal Amsili Introduction (1) a. Jones loves a woman. Davidson b. ∃ x woman( x ) ∧ love( j , x ) Initial Problem 1 Initial Problem 2 Reification Discussion would equally represent Parsons Kamp&Reyle The question (2) a. Jones loved a woman. Observations and arguments b. Jones will love a woman. Complete Proposal as well as Conclusion & Perspectives (3) a. Jones used to love a woman. References b. Jones was loving a woman. 4 / 40

The Negation Time Representation of Events Pascal Amsili Introduction (1) a. Jones loves a woman. Davidson b. ∃ x woman( x ) ∧ love( j , x ) Initial Problem 1 Initial Problem 2 Reification Discussion would equally represent Parsons Kamp&Reyle The question (2) a. Jones loved a woman. Observations and arguments b. Jones will love a woman. Complete Proposal as well as Conclusion & Perspectives (3) a. Jones used to love a woman. References b. Jones was loving a woman. Yet we want (4) not to be contradictory. (4) Jones loved a women and he doesn’t love a woman. 4 / 40

The Negation Time Representation: temporal logic of Events Variant of modal logic: propositional operators & accessibility Pascal Amsili relation between worlds Introduction Davidson Initial Problem 1 Initial Problem 2 Reification Discussion Parsons Kamp&Reyle The question Observations and arguments Complete Proposal Conclusion & Perspectives References 5 / 40

The Negation Time Representation: temporal logic of Events Variant of modal logic: propositional operators & accessibility Pascal Amsili relation between worlds Introduction Davidson P [ Ψ ] = there is a world w in the past s.t. Ψ ∈ w . Initial Problem 1 Initial Problem 2 Reification (5) a. Jones loved a woman. Discussion Parsons b. P [ ∃ x woman( x ) ∧ love( j , x )] Kamp&Reyle The question Observations and arguments Complete Proposal Conclusion & Perspectives References 5 / 40

The Negation Time Representation: temporal logic of Events Variant of modal logic: propositional operators & accessibility Pascal Amsili relation between worlds Introduction Davidson P [ Ψ ] = there is a world w in the past s.t. Ψ ∈ w . Initial Problem 1 Initial Problem 2 Reification (5) a. Jones loved a woman. Discussion Parsons b. P [ ∃ x woman( x ) ∧ love( j , x )] Kamp&Reyle The question Observations P [ Ψ ] = there is a world w in the future s.t. Ψ ∈ w . and arguments Complete (6) a. Jones will love a woman. Proposal b. F [ ∃ x woman( x ) ∧ love( j , x )] Conclusion & Perspectives References 5 / 40

The Negation Time Representation: temporal logic of Events Variant of modal logic: propositional operators & accessibility Pascal Amsili relation between worlds Introduction Davidson P [ Ψ ] = there is a world w in the past s.t. Ψ ∈ w . Initial Problem 1 Initial Problem 2 Reification (5) a. Jones loved a woman. Discussion Parsons b. P [ ∃ x woman( x ) ∧ love( j , x )] Kamp&Reyle The question Observations P [ Ψ ] = there is a world w in the future s.t. Ψ ∈ w . and arguments Complete (6) a. Jones will love a woman. Proposal b. F [ ∃ x woman( x ) ∧ love( j , x )] Conclusion & Perspectives (7) a. PP [ Ψ ] References 5 / 40

The Negation Time Representation: temporal logic of Events Variant of modal logic: propositional operators & accessibility Pascal Amsili relation between worlds Introduction Davidson P [ Ψ ] = there is a world w in the past s.t. Ψ ∈ w . Initial Problem 1 Initial Problem 2 Reification (5) a. Jones loved a woman. Discussion Parsons b. P [ ∃ x woman( x ) ∧ love( j , x )] Kamp&Reyle The question Observations P [ Ψ ] = there is a world w in the future s.t. Ψ ∈ w . and arguments Complete (6) a. Jones will love a woman. Proposal b. F [ ∃ x woman( x ) ∧ love( j , x )] Conclusion & Perspectives (7) a. PP [ Ψ ] ≈ pluperfect References 5 / 40

The Negation Time Representation: temporal logic of Events Variant of modal logic: propositional operators & accessibility Pascal Amsili relation between worlds Introduction Davidson P [ Ψ ] = there is a world w in the past s.t. Ψ ∈ w . Initial Problem 1 Initial Problem 2 Reification (5) a. Jones loved a woman. Discussion Parsons b. P [ ∃ x woman( x ) ∧ love( j , x )] Kamp&Reyle The question Observations P [ Ψ ] = there is a world w in the future s.t. Ψ ∈ w . and arguments Complete (6) a. Jones will love a woman. Proposal b. F [ ∃ x woman( x ) ∧ love( j , x )] Conclusion & Perspectives (7) a. PP [ Ψ ] ≈ pluperfect References b. FP [ Ψ ] 5 / 40

The Negation Time Representation: temporal logic of Events Variant of modal logic: propositional operators & accessibility Pascal Amsili relation between worlds Introduction Davidson P [ Ψ ] = there is a world w in the past s.t. Ψ ∈ w . Initial Problem 1 Initial Problem 2 Reification (5) a. Jones loved a woman. Discussion Parsons b. P [ ∃ x woman( x ) ∧ love( j , x )] Kamp&Reyle The question Observations P [ Ψ ] = there is a world w in the future s.t. Ψ ∈ w . and arguments Complete (6) a. Jones will love a woman. Proposal b. F [ ∃ x woman( x ) ∧ love( j , x )] Conclusion & Perspectives (7) a. PP [ Ψ ] ≈ pluperfect References b. FP [ Ψ ] ≈ past in the future 5 / 40

The Negation Time Representation: temporal logic of Events Variant of modal logic: propositional operators & accessibility Pascal Amsili relation between worlds Introduction Davidson P [ Ψ ] = there is a world w in the past s.t. Ψ ∈ w . Initial Problem 1 Initial Problem 2 Reification (5) a. Jones loved a woman. Discussion Parsons b. P [ ∃ x woman( x ) ∧ love( j , x )] Kamp&Reyle The question Observations P [ Ψ ] = there is a world w in the future s.t. Ψ ∈ w . and arguments Complete (6) a. Jones will love a woman. Proposal b. F [ ∃ x woman( x ) ∧ love( j , x )] Conclusion & Perspectives (7) a. PP [ Ψ ] ≈ pluperfect References b. FP [ Ψ ] ≈ past in the future c. PFFPPFP [ Ψ ] 5 / 40

The Negation Time Representation: temporal logic of Events Variant of modal logic: propositional operators & accessibility Pascal Amsili relation between worlds Introduction Davidson P [ Ψ ] = there is a world w in the past s.t. Ψ ∈ w . Initial Problem 1 Initial Problem 2 Reification (5) a. Jones loved a woman. Discussion Parsons b. P [ ∃ x woman( x ) ∧ love( j , x )] Kamp&Reyle The question Observations P [ Ψ ] = there is a world w in the future s.t. Ψ ∈ w . and arguments Complete (6) a. Jones will love a woman. Proposal b. F [ ∃ x woman( x ) ∧ love( j , x )] Conclusion & Perspectives (7) a. PP [ Ψ ] ≈ pluperfect References b. FP [ Ψ ] ≈ past in the future c. PFFPPFP [ Ψ ] ??? 5 / 40

The Negation Time Representation: temporal logic of Events Variant of modal logic: propositional operators & accessibility Pascal Amsili relation between worlds Introduction Davidson P [ Ψ ] = there is a world w in the past s.t. Ψ ∈ w . Initial Problem 1 Initial Problem 2 Reification (5) a. Jones loved a woman. Discussion Parsons b. P [ ∃ x woman( x ) ∧ love( j , x )] Kamp&Reyle The question Observations P [ Ψ ] = there is a world w in the future s.t. Ψ ∈ w . and arguments Complete (6) a. Jones will love a woman. Proposal b. F [ ∃ x woman( x ) ∧ love( j , x )] Conclusion & Perspectives (7) a. PP [ Ψ ] ≈ pluperfect References b. FP [ Ψ ] ≈ past in the future c. PFFPPFP [ Ψ ] ??? very powerfull (Kamp, 1979) ⇒ what about present tense? aspect? 5 / 40

The Negation Time Representation: temporalized predicates of Events Pascal Amsili Introduction Davidson Initial Problem 1 Initial Problem 2 Reification Discussion Parsons Kamp&Reyle (8) a. Jones loved a woman. The question b. ∃ t ∃ x t < n ∧ woman( x ) ∧ love( j , x , t ) Observations and arguments Complete I Predicates have one additional place for time Proposal Conclusion & I Underspecified role of the time argument Perspectives References 6 / 40

The Negation Time Representation: second order formulae of Events Pascal Amsili Introduction Davidson Initial Problem 1 Initial Problem 2 Reification Discussion Parsons (9) a. Jones loves a woman. Kamp&Reyle The question b. ∃ t t < n holds at ( t , [ ∃ x woman( x ) ∧ love( j , x )]) Observations and arguments I usual in AI/KR Complete Proposal I too powerfull (decidability issues) Conclusion & Perspectives I many meaning postulates needed References 7 / 40