Proceedings of SALT 26: 325–349, 2016 Expressing permission* William B. Starr Cornell University Abstract This paper proposes a semantics for free choice permission that explains both the non-classical behavior of modals and disjunction in sentences used to grant permission, and their classical behavior under negation. It also explains why permissions can expire when new information comes in and why free choice arises even when modals scope under disjunction. On the proposed approach, deontic modals update preference orderings, and connectives operate on these updates rather than propositions. The success of this approach stems from its capacity to capture the difference between expressing the preferences that give rise to permissions and conveying propositions about those preferences. Keywords: Free choice permission, modality, dynamic semantics, expressive meaning 1 Free choice permission and allied phenomena While I will focus on deontic modals here, free choice effects arise in non-deontic and even non-modal contexts too (Fox 2007). As I will discuss in §3, once my analysis is stated it will be possible to articulate structural parallels across this wider range of data. In this section I will lay out the data to Expressing permission and logic for may that captures free choice effects. Negation and DP are treated in §2.4. Section 2.5 uses these tools to explain RS1–6 and §2.6 returns to the issue of how ignorance and uncooperativeness can defeat free choice effects. 2.1 Information dynamics The dynamics of information is simple. Information says the world is some of these ways, and none of those. This is captured by taking a state of information s to be a set of worlds. If one assumes a sentence’s only job is to provide information about the world, then a sentence φ’s meaning[φ] can be thought of as a function from one state of information s to another s′. In Veltman’s (1996) terminology,s[φ]is the result of updating s with φ. On this dynamic approach, an atomic sentence A serves to eliminate worlds from s where A is false. ¬φ removes worlds that would survive AB aB Ab ab [A] /leftrightline→ AB aB Ab ab {wAB,wAb,waB,wab} { wAB,wAb} Figure 1 Atomic Update (Uppercase = True, Lowercase = False) an update with φ, while φ∧ψ sequences the effects of its conjuncts. φ∨ψ unions the effects of its conjuncts. More formally: Informational Update Semantics (Veltman 1996) 1. s[A]={w∈s/divides.alt0w(A)= 1} 3. s[φ∧ψ]=(s[φ])[ψ] 2. s[¬φ]= s−s[φ] 4. s[φ∨ψ]= s[φ]∪s[ψ] Adding deontic modals to this framework presents a choice: do deontic modals provide information about the world, and so update s, or do they have a different kind of effect entirely? The traditional approach in modal logic has been to assume that deontic modals provide information about the world. 3φ eliminates any world w relative to which there is not an accessible φ-world. On this analysis 3φ provides information about the world, namely which worlds are accessible from our world. Veltman 1996 offers a slightly different approach to Mightφ, where it does not point-wise eliminate worlds based on their properties, but places a global test on the information state itself. The result of the test is s or/uni2205. Test Semantics for Might s[Mightφ]={w∈s/divides.alt0s[φ]≠/uni2205} 331 Expressing permission Synthese 147(2). 343–377. doi:10.1007/s11229-005-1353-y. Simons, Mandy. 2005. Dividing things up: The semantics of or and the modal/or interaction. Natural Language Semantics 13(3). 271–316. doi:10.1007/s11050- 004-2900-7. Sloman, Steven. 2005. Causal Models: How People Think About the World and Its Alternatives. New York: OUP. Stalnaker, Robert C. 1981. A defense of conditional excluded middle. In William L. Harper, Robert Stalnaker & Glenn Pearce (eds.), Ifs: Conditionals, Belief, Decision, Chance, and Time, 87–104. Dordrecht: D. Reidel Publishing Co. Starr, William B. 2016a. Dynamic expressivism about deontic modality. In N. Char- low & M. Chrisman (eds.), Deontic Modality , 355–394. New York: Oxford University Press. doi:10.1093/acprof:oso/9780198717928.003.0013. Starr, William B. 2016b. A preference semantics for imperatives. Under Review at Semantics & Pragmatics. Tieu, Lyn, Jacopo Romoli, Peng Zhou & Stephen Crain. 2016. Children’s knowledge of free choice inferences and scalar implicatures. Journal of Semantics 33(2). 269–298. doi:10.1093/jos/ffv001. Van Fraassen, Bas C. 1966. Singular terms, truth-value gaps and free logic. Journal of Philosophy 3. 481–495. doi:10.2307/2024549. Veltman, Frank. 1996. Defaults in update semantics. Journal of Philosophical Logic 25(3). 221–261. doi:10.1007/BF00248150. von Wright, Georg Henrik. 1968. Deontic logic and the theory of conditions.Crítica: Revista Hispanoamericana de Filosofía 2(6). 3–31. http://www.jstor.org/stable/ 40103910. Willer, Malte. 2015. Simplifying counterfactuals. In Thomas Brochhagen, Floris Roelofsen & Nadine Theiler (eds.), 20th Amsterdam Colloquium, 428– 437. Amsterdam: ILLC. http://semanticsarchive.net/Archive/mVkOTk2N/ AC2015-proceedings.pdf. Zimmermann, Thomas Ede. 2000. Free choice disjunction and epistemic possibility. Natural Language Semantics 8(4). 255–290. doi:10.1023/A:1011255819284. William B. Starr 218 Goldwin Smith Hall Cornell University Ithaca, NY 14853 will.starr@cornell.edu 349