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Lorenzen Won the Game, Lorenz Did Too: Dialogical Logic for Ellipsis and Anaphora Resolution

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Logic, Language, Information, and Computation (WoLLIC 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 13038))

Abstract

We propose a novel solution to anaphora and ellipsis resolution using multi-sorted first order logic. Our theory is proof-theoretic, employing methods from the study of dialogical logic. The first order propositions are extracted from reduced lambda terms, which are themselves derived from Lambek Categorial Grammar proofs.

Authors contributed equally and are listed in alphabetic order.

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Notes

  1. 1.

    VPE doesn’t describe the whole distribution of PAE, since, unless one extends the notion of VP well beyond its descriptive use, the antecedents for PAE need not be VPs. See [24] for excellent descriptive discussion of the distribution of ellipsis in English.

  2. 2.

    Note we write \(Q x_i,...,x_n.P\) for \(Qx_i...Qx_n.P\).

  3. 3.

    We do not not employ equality or functions in the logic. Both of these devices could be added to the logic, but we prefer to use the simplest system–the one without these devices–for expository purposes. There might be independent need for functions and even second order quantification over functions, depending on how one conceives of ‘strict’ versus ‘sloppy’ anaphoric reference, but we will not discuss this topic further here.

  4. 4.

    See [43] for an overview of some of the uses of events in linguistics and philosophy. [44] divided events into various subtypes: achievments, activities, accomplishments, and states. We will not be concerned with subtyping events in the present paper.

  5. 5.

    This dependence is explicitly modelled in (12), where the theme is recovered iff the event proper of the antecedent involved a theme.

  6. 6.

    One could extend our theory to ACG or any of the other Curry-esque Categorial Grammars [30, 34, 40] which can express syntactic dependencies which cannot be expressed in LCG without modifying the underlying type-logic.

  7. 7.

    John’s sleeping could be modified by the expression ‘well’, which would correspond to \(V \backslash V\). Since multiple adjuncts are possible for most verbs, the term for ‘well’ would be \(\lambda P^{(v \rightarrow i\rightarrow t)\rightarrow v\rightarrow t},R^{v\rightarrow i\rightarrow t},w^v.[P(\lambda u^v,k^i.well(q,k) \wedge R(q,k),w)]^t\).

  8. 8.

    If there were more possible antecedents, more axioms would be needed to pick among those antecedents or else the strongest proposition to be proved would be a disjunction, with each disjunct corresponding to the proposition proved here modulo the choice of antecedent.

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Authors and Affiliations

  1. LIRMM Université de Montpellier, Montpellier, France

    Davide Catta

  2. CNRS, Paris, France

    Davide Catta

  3. Department of Linguistics, The Ohio State University, Columbus, USA

    Symon Jory Stevens-Guille

Authors
  1. Davide Catta
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Correspondence to Davide Catta .

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Editors and Affiliations

  1. Cornell University, New York, NY, USA

    Alexandra Silva

  2. Instituto de Matematica e Estatisrica, Universidade de São Paulo, Sao Paulo, São Paulo, Brazil

    Renata Wassermann

  3. Centro de Informática, Universidade Federal de Pernambuco, Recife, Pernambuco, Brazil

    Ruy de Queiroz

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Catta, D., Stevens-Guille, S.J. (2021). Lorenzen Won the Game, Lorenz Did Too: Dialogical Logic for Ellipsis and Anaphora Resolution. In: Silva, A., Wassermann, R., de Queiroz, R. (eds) Logic, Language, Information, and Computation. WoLLIC 2021. Lecture Notes in Computer Science(), vol 13038. Springer, Cham. https://doi.org/10.1007/978-3-030-88853-4_17

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