A semantic interpretation of modality in counterfactual conditionals

Abstract

This paper provides a background on the role of world knowledge in disambiguating modals and proposes treating the disambiguation of counterfactuals as a slightly more tractable sub-case of the general problem. Using a model theoretic possible worlds approach, counterfactuals are disambiguated with respect to a world of evaluation resembling classic Formal Semantic treatments (e.g., Kratzer 1977, 1981, 1989; Lewis 1973; Veltman 2005). The world, which provides a context of evaluation, is located through the interaction of the antecedent and consequent propositions with world knowledge axioms. This approach to modal disambiguation provides a connection between a grammar and the type of inferences typically handled in Knowledge Representation Systems (e.g., Hobbs et al. 1990) in a limited domain. The model theoretic semantics are linked with typed feature structures in an HPSG syntax (Pollard and Sag 1994). This grammar is implemented in TRALE, Penn's (2004) Prolog-based framework for typed feature structure grammar development. The compositional semantics in TRALE is specified in Penn and Richters' (2004, 2005) Constraint Language for Lexical Resource Semantics (CLLRS). This semantic component provides a semantic parse in which heads and arguments are combined systematically and the scope of negation or quantification can be accurately reflected. In the case of counterfactuals, the CLLRS semantic parse is passed to a model-theoretic interpreter. The mapping between the CLLRS semantic parse and the well-formed formulas of the model is defined by checking the parseability of the formula in the compositional semantics. Sets of possible worlds interact with constraints on world knowledge and constraints defining counterfactual validity. The truth value for a counterfactual is returned to the grammar relative to a context of evaluation. The results of counterfactual evaluation are returned in a form consistent with the grammar's internal compositional semantics. By the method described above, the interpreter provides a grammar-external component in which inferences involving world knowledge have the potential to be more efficiently evaluated. Through the development of model-checking techniques, for instance, it could be shown whether or not well-formed formulas and constraints hold in larger models and move towards capturing more fine-grained modal inferences in a larger domain.