Contextual Logic With Modalities for Time and Space

Abstract

We develop a formal apparatus to be used as a tool in analyzing common kinds of context dependence in natural language, and their interaction with temporal and spatial modalities. It is based on context-operators, which act on wffs. The interplay between the various modalities and the context-operators is one of the main targets of the analysis. Statements made by different people at different times in different places, using the same personal temporal and spatial indexicals, can be represented in the system, and can be combined by sentential connectives and be subject to quantification. The use of spatial modality and the suggested treatment of adverbial phrases are new as far as we know. So is a certain variant of temporal modality. In the nontechnical part, consisting of Sections 1 and 2, we discuss the role that formalisms can, in principle, play in the analysis of linguistic usage; this is followed by a philosophical discussion of various kinds of context dependence. The semitechnical part, Section 3, introduces the system's components, the context, and the modal operators, and explains their use via natural language examples. In Section 4 the formal language and its semantics are defined, in full detail. The temporal and spatial sublanguages constitute separate sorts, which interact through the modal operators and the context-operators. A sound deductive system is given and a completeness result is stated, without proof.

Vagueness, tolerance and contextual logic

“…in a paper on contextuality, Gaifman (2008). There is no overlap between that paper and the present one.…”

“…But in LD, whose aim is purely philosophical, the impossibility of treating statements by different speakers who employ the word 'I' is a serious limitation, which can be amended by incorporating context operators. In Gaifman (2008) there is a system that incorporates, among other things, context operators for proper names and various indexicals.…”