David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
As we’ve seen in the last chapter, there is good linguistic reason to categorize negations (and negative operators in general) by which De Morgan laws they support. The weakest negative operators (merely downward monotonic) support only two De Morgan laws;1 medium-strength negative operators support a third;2 and strong negative operators support all four. As we’ve also seen, techniques familiar from modal logic are of great use in giving unifying theories of negative operators. In particular, Dunn’s (1990) distributoid theory allows us to generate relational semantics for many negations. However, the requirements of distributoid theory are a bit too strict for use in modeling the weakest negations. For a relational semantics to work, an operator must either distribute or antidistribute over either conjunction or disjunction; but the merely downward monotonic operators do not. Thus, a unifying semantics cannot be had in distributoid theory. In the (more familiar) study of positive modalities, there is a parallel result. Normal necessities distribute over conjunction, and normal possibilities over disjunction. When these distributions break down, a relational semantics is no longer appropriate. Here, there is a somewhat familiar solution: neighborhood semantics. In this chapter, I’ll adapt neighborhood semantics to the less familiar case of negative modalities, showing how it can be used to give a single semantic framework appropriate to all the pertinent sorts of negative operators.
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library||
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Dominic Gregory (2001). Completeness and Decidability Results for Some Propositional Modal Logics Containing “Actually” Operators. Journal of Philosophical Logic 30 (1):57-78.
Lenny Clapp (2009). The Problem of Negative Existentials Does Not Exist: A Case for Dynamic Semantics. Journal of Pragmatics 41 (7):1422-1434.
Graham Priest (2009). Neighborhood Semantics for Intentional Operators. Review of Symbolic Logic 2 (2):360-373.
Horacio Arló-Costa & Eric Pacuit (2006). First-Order Classical Modal Logic. Studia Logica 84 (2):171 - 210.
Gonzalo E. Reyes & Houman Zolfaghari (1996). Bi-Heyting Algebras, Toposes and Modalities. Journal of Philosophical Logic 25 (1):25 - 43.
Seth Yalcin (2007). Epistemic Modals. Mind 116 (464):983-1026.
J. Michael Dunn & Chunlai Zhou (2005). Negation in the Context of Gaggle Theory. Studia Logica 80 (2-3):235 - 264.
Added to index2010-06-08
Total downloads26 ( #70,326 of 1,100,036 )
Recent downloads (6 months)3 ( #127,210 of 1,100,036 )
How can I increase my downloads?