A formal approach to vague expressions with indexicals - Martens, Liesbeth; Primiero, Giuseppe (Logic and Engineering of Natural Language Semantics 9 (LENLS 9-2012), 2012)
In this paper, we offer a formal approach to the scantily investigated problem of vague expressions with indexicals, in particular including the spatial indexical `here' and the temporal indexical `now'. We present two versions of an adaptive fuzzy logic extended with an indexical, formally expressed by a modifier as a function that applies to predicative formulas. In the first version, such an operator is applied to non-vague predicates. The modified formulas may have a fuzzy truth value and fit into a Sorites paradox. We use adaptive fuzzy logics as a reasoning tool to address such a paradox. The modifier enables us to offer an adequate explication of the dynamic reasoning process. In the second version, a different result is obtained for an indexical applied to a formula with a possibly vague predicate, where the resulting modified formula has a crisp value and does not add up to a Sorites paradox.