About Modal Subordination A Montagovian Treatment Discussion and Alternative Proposals Conclusion 1 / 15 Semantic Representation of Modal Subordination Using Type Theory Nicholas Asher 1 Sylvain Pogodalla 2 1 asher@irit.fr CNRS, IRIT 2 sylvain.pogodalla@loria.fr LORIA/INRIA Nancy–Grand Est December 14 2009
About Modal Subordination A Montagovian Treatment Discussion and Alternative Proposals Conclusion 2 / 15 Outline About Modal Subordination 1 A Montagovian Treatment 2 Discussion and Alternative Proposals 3 Conclusion 4
About Modal Subordination A Montagovian Treatment Discussion and Alternative Proposals Conclusion 3 / 15 Modal Subordination: Some Examples Example 1 A wolf might walk in. It would growl.
About Modal Subordination A Montagovian Treatment Discussion and Alternative Proposals Conclusion 3 / 15 Modal Subordination: Some Examples Example 1 A wolf might walk in. It would growl. 2 A wolf might walk in. ∗ It will growl.
About Modal Subordination A Montagovian Treatment Discussion and Alternative Proposals Conclusion 3 / 15 Modal Subordination: Some Examples Example 1 A wolf might walk in. It would growl. 2 A wolf might walk in. ∗ It will growl. 3 A wolf walks in. It would growl.
About Modal Subordination A Montagovian Treatment Discussion and Alternative Proposals Conclusion 3 / 15 Modal Subordination: Some Examples Example 1 A wolf might walk in. It would growl. 2 A wolf might walk in. ∗ It will growl. 3 A wolf walks in. It would growl. References: DRT and Dynamic Frameworks Accommodation of DRSs [Roberts(1989)] Modals presuppose their domain [Geurts(1999)] Anaphoric context references and graded modality [Frank and Kamp(1997)] Compositional DRT extension [Stone and Hardt(1997)] Two-dimensionsal approach, accessibility relation and world ordering [van Rooij(2005)] DPL and sets of epistemic possibilities [Asher and McCready(2007)]
About Modal Subordination A Montagovian Treatment Discussion and Alternative Proposals Conclusion 4 / 15 DRT Based Account Example A wolf might walk in.
About Modal Subordination A Montagovian Treatment Discussion and Alternative Proposals Conclusion 4 / 15 DRT Based Account Example A wolf might walk in. x ♦ wolf ( x ) enter ( x )
About Modal Subordination A Montagovian Treatment Discussion and Alternative Proposals Conclusion 4 / 15 DRT Based Account Example A wolf might walk in.It would growl. x ♦ wolf ( x ) enter ( x )
About Modal Subordination A Montagovian Treatment Discussion and Alternative Proposals Conclusion 4 / 15 DRT Based Account Example A wolf might walk in.It would growl. x ♦ wolf ( x ) enter ( x ) y � growl ( y )
About Modal Subordination A Montagovian Treatment Discussion and Alternative Proposals Conclusion 4 / 15 DRT Based Account Example A wolf might walk in.It would growl. x ♦ wolf ( x ) enter ( x ) y � growl ( y ) Note: Accessibility conditions
About Modal Subordination A Montagovian Treatment Discussion and Alternative Proposals Conclusion 4 / 15 DRT Based Account Example A wolf might walk in.It would growl. x x ♦ wolf ( x ) ♦ wolf ( x ) enter ( x ) enter ( x ) y � growl ( y ) Note: Accessibility conditions
About Modal Subordination A Montagovian Treatment Discussion and Alternative Proposals Conclusion 4 / 15 DRT Based Account Example A wolf might walk in.It would growl. x x ♦ wolf ( x ) ♦ wolf ( x ) enter ( x ) enter ( x ) x y y � � wolf ( x ) growl ( y ) growl ( y ) enter ( x ) Note: Accessibility conditions
About Modal Subordination A Montagovian Treatment Discussion and Alternative Proposals Conclusion 4 / 15 DRT Based Account Example A wolf might walk in.It would growl. x x ♦ wolf ( x ) ♦ wolf ( x ) enter ( x ) enter ( x ) x y y � � wolf ( x ) growl ( y ) growl ( y ) enter ( x ) Note: Accessibility conditions Modal base and accommodation
About Modal Subordination A Montagovian Treatment Discussion and Alternative Proposals Conclusion 5 / 15 A Montagovian Treatment Our Aim To consider modal subordination in [de Groote(2006)]’s framework: Taking advantages of this framework Implementing MS principles in lexical entries Without any change to the formal framwork The Steps Intepretation of (the syntactic type of) the sentences Combination rules The lexical semantics of MS
About Modal Subordination A Montagovian Treatment Discussion and Alternative Proposals Conclusion 6 / 15 Interpretation of the Sentences [de Groote(2006)]: � s � = γ → ( γ → t ) → t
About Modal Subordination A Montagovian Treatment Discussion and Alternative Proposals Conclusion 6 / 15 Interpretation of the Sentences [de Groote(2006)]: � s � = γ → ( γ → t ) → t Here: � s � = γ → γ → ( γ → γ → t ) → ( γ → γ → t ) → ( t → t → t ) → t
About Modal Subordination A Montagovian Treatment Discussion and Alternative Proposals Conclusion 6 / 15 Interpretation of the Sentences [de Groote(2006)]: � s � = γ → ( γ → t ) → t Here: � s � = γ → γ → ( γ → γ → t ) → ( γ → γ → t ) → ( t → t → t ) → t A modal environment and a factual environment
About Modal Subordination A Montagovian Treatment Discussion and Alternative Proposals Conclusion 6 / 15 Interpretation of the Sentences [de Groote(2006)]: � s � = γ → ( γ → t ) → t Here: � s � = γ → γ → ( γ → γ → t ) → ( γ → γ → t ) → ( t → t → t ) → t A modal environment and a factual environment A modal continuation and a factual continuation (or a modal contribution and a factual contribution of the continuation)
About Modal Subordination A Montagovian Treatment Discussion and Alternative Proposals Conclusion 6 / 15 Interpretation of the Sentences [de Groote(2006)]: � s � = γ → ( γ → t ) → t Here: � s � = γ → γ → ( γ → γ → t ) → ( γ → γ → t ) → ( t → t → t ) → t A modal environment and a factual environment A modal continuation and a factual continuation (or a modal contribution and a factual contribution of the continuation) a modal part and a factual part
About Modal Subordination A Montagovian Treatment Discussion and Alternative Proposals Conclusion 6 / 15 Interpretation of the Sentences [de Groote(2006)]: � s � = γ → ( γ → t ) → t Here: � s � = γ → γ → ( γ → γ → t ) → ( γ → γ → t ) → ( t → t → t ) → t A modal environment and a factual environment A modal continuation and a factual continuation (or a modal contribution and a factual contribution of the continuation) a modal part and a factual part Note on pairs: ( t , t ) as ( t → t → t ) → t A pair ( a , b ) is interpreted as λ f . f a b (selecting two-place functions and applying them to the 1st and the 2nd component) An additional parameter: How should the modal and the factual part be combined? Typically λ b 1 b 2 . b 1 ∧ b 2 When should they be combined? Possibility of a Reset operator that close the modal contribution.
About Modal Subordination A Montagovian Treatment Discussion and Alternative Proposals Conclusion 6 / 15 Interpretation of the Sentences [de Groote(2006)]: � s � = γ → ( γ → t ) → t Here: � s � = γ → γ → ( γ → γ → t ) → ( γ → γ → t ) → ( t → t → t ) → t A modal environment and a factual environment A modal continuation and a factual continuation (or a modal contribution and a factual contribution of the continuation) a modal part and a factual part � np � = ( e → � s � ) → � s � , � n � = e → � s � , etc. Note on pairs: ( t , t ) as ( t → t → t ) → t A pair ( a , b ) is interpreted as λ f . f a b (selecting two-place functions and applying them to the 1st and the 2nd component) An additional parameter: How should the modal and the factual part be combined? Typically λ b 1 b 2 . b 1 ∧ b 2 When should they be combined? Possibility of a Reset operator that close the modal contribution.
About Modal Subordination A Montagovian Treatment Discussion and Alternative Proposals Conclusion 7 / 15 Combinations S 1 . S 2 when S 2 has a factual mood � S 1 . S 2 � = λ i 1 i 2 k 1 k 2 f . � S 1 � i 1 i 2 k 1 ( λ i ′ 1 i ′ 2 . � S 2 � i ′ 1 i ′ 2 k 1 k 2 Π 2 ) f (with Π 2 = λ ab . b the second projection)
About Modal Subordination A Montagovian Treatment Discussion and Alternative Proposals Conclusion 7 / 15 Combinations S 1 . S 2 when S 2 has a factual mood � S 1 . S 2 � = λ i 1 i 2 k 1 k 2 f . � S 1 � i 1 i 2 k 1 ( λ i ′ 1 i ′ 2 . � S 2 � i ′ 1 i ′ 2 k 1 k 2 Π 2 ) f (with Π 2 = λ ab . b the second projection) S 1 . S 2 when S 2 has a nonfactual mood � S 1 . S 2 � = λ i 1 i 2 k 1 k 2 f . � S 1 � i 1 i 2 ( λ i ′ 1 i ′ 2 . � S 2 � i ′ 1 i ′ 2 k 1 k 2 Π 1 ) k 2 f (with Π 1 = λ ab . a the first projection)
About Modal Subordination A Montagovian Treatment Discussion and Alternative Proposals Conclusion 8 / 15 Example � S 1 . S 2 � = λ i 1 i 2 k 1 k 2 f . � S 1 � i 1 i 2 k 1 ( λ i ′ 1 i ′ 2 . � S 2 � i ′ 1 i ′ 2 k 1 k 2 Π 2 ) f Example � A wolf might walk in � = λ i 1 i 2 k 1 k 2 f . f ( ♦ ( ∃ x . ( wolf x ) ∧ (( enter x ) ∧ ( k 1 ( x :: i 1 ) i 2 )))) ( k 2 i 1 i 2 )
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