A formal approach to vague expressions with indexicals

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

Three-Valued Plurivaluationism and the Higher-Order Vagueness

Plurivaluationism is an approach to solving the Sorites Paradox based on the idea that vague discourse has more than one acceptable interpretation. Since plurivaluationism is a framework which enables one to utilize different underlying logics, three basic versions can be identified – bivalent, many-valued and fuzzy. The aim of this paper is to show how three-valued plurivaluationism, as proposed by Wang, fares against its competitors. In the first and second part, some of the traditional approaches to solving the Sorites Paradox are outlined and are confronted with two objections based on the problem of higher-order vagueness – the so-called location problem and the jolt problem. The third part is dedicated to introducing and evaluating different versions of plurivaluationism, with an emphasis on comparing Wang’s three-valued plurivaluationism to its competitors. While three-valued plurivaluationism is a promising enterprise, I show that some modifications Wang made to his system cause the location problem in plurivaluationism to re-emerge, and it also fails to provide a satisfactory answer to the jolt problem

Modeling sorites reasoning with adaptive fuzzy logic

We present and discuss a new solution for reasoning with sorites series and their related paradoxes. We argue that a suitable logic for sorites series should be able to apply specific classical logic rules like modus ponens until and unless it becomes apparent that these applications generate unacceptable results. When the latter happens, the logic should be able to retract those applications of classical logic rules that are problematic. The formal core of our solution consists of several adaptive logics based on a Łukasiewicz fuzzy logic extended with the Baaz’Δ-operator and a non-singleton interval of designated values. The natural dynamics characteristic of adaptive logics allows these logics to perform necessary retractions in an intuitive and elegant manner