A Dynamic-Epistemic-Logical Explanation of
Presupposition Projection
鈴木 聡 (Satoru SUZUKI)
駒澤大学総合教育研究部非常勤講師

Presupposition projection is one of the much-discussed subjects in the fields of philosophyof language and linguistics. According to Beaver et al. [3], the following at least ten lexicalclasses constructions are widely agreed to be presupposition triggers: (i) factives, (ii) aspectualverbs, (iii) temporal clauses headed by “before”, “after”, “since”, etc., (iv) manner adverbs,(v) sortally restricted predicates of various categories, (vi) cleft sentences, (vii) quantifiers,(viii) definite descriptions, (ix) names, and (x) intonation. In this talk, we focus on (i),(ii)and (v). In (1)-(5), the presupposition that John used to smoke is canceled: (1) John used
to smoke and he stopped smoking. (2) If John used to smoke, then he stopped smoking. (3)John did not use to smoke or he stopped smoking. (4) John used to smoke or he stoppedsmoking. (5) John used to smoke and Mary knows that John used to smoke. In (6)-(10),the presupposition is projected (inherited): (6) John did not stop smoking. (7) If John
moved to Japan, then he stopped smoking. (8) John did not moved to Japan or he stoppedsmoking. (9) John is a bachelor. (10) Mary does not knows that John used to smoke. We callthis the cancellation/inheritance phenomena of presupposition (CIP). Dynamic semantics is
one of the most well-known models for explaining CIP. Stalnaker [8] observes that a context
plays an essential role in presupposition and that presupposition is based on common ground(common knowledge). In (6)-(10), each context requires that it is common knowledge thatJohn used to smoke. On the other hand, in (1)-(5), it does not. Heim [5] is one of thepioneering works on dynamic semantics. Heim considers that a context plays an essential rolein presupposition and adopts a kind of the dynamic view of meaning: The semantic value ofa sentence is a context change potential (CCP). The dynamic view forms a contrast with thestatic view: The semantic value of a sentence is its truth condition. Soames [7] points out
the explanatory incompleteness problem of Heim’s dynamic semantics. Dynamic epistemic
logic (DEL) (cf. [1]) shares dynamic-semantic factor with dynamic semantics. Rothschild andYalcin [6] discuss the status of dynamic-semantic factor in theoretical analyses of linguistic
phenomena. The aim of this talk is to give solutions to Problem 1: What is the dynamicsemantic factor necessary to express presupposition projection when we adopt the languageof DEL that holds the static view of meaning and so avoids the explanatory incompleteness1

problem as a language fragment that contains such a factive as “know” and such an aspectual
verb as “stop”? and Problem 2: How can we give a DEL explanation of CIP?. In DEL,[ψ]φ expresses the statement φ is true after a public announcement ψ. To evaluate [ψ]φ ata pointed Kripke model (M, w), we transform M according to the prescriptions of ψ andthen obtain a new model (M′ , w′ ) at which we evaluate φ. So DEL holds the static viewof meaning, whereas it has a dynamic semantics across model transformations. In DEL, thechanges of context are modeled by model transformations. Although van Eijck and Unger [4]formalize presupposition projection about (v) sortally restricted predicates above in terms ofDEL, they do not deal with CIP. In this talk, according to van Eijck and Unger [4], we modela presupposition φ as a public announcement “it is common knowledge between a speakerand her hearer that φ” ([Cs,h (φ)]), and as a system of DEL we use Public Announce Logic
with common knowledge between a speaker and her hearer (PAL + Cs,h ). Baltag et al. [2]prove the following theorems: Fact 1 (Reduction) Every wﬀ (well-formed formula) φ in
the language of PAL without common knowledge is equivalent in PAL to a wﬀ φ◦ in the publicannouncement-free fragment. Fact 2 (Irreducibility) It is not possible to find any publicannouncement-free equivalent of each wﬀ of PAL + Cs,h . We can derive the next corollary
from Facts 1 and 2: Corollary 1 (Necessary Dynamic-Semantic Factor) The dynamicsemantic factor necessary to express presupposition projection when we adopt the language ofDEL is only a model transformation based on [Cs,h (φ)] that models a presupposition but not
any types of semantic changes of logical connectives. Corollary 1 gives a solution to Problem
1. However, DEL alone cannot deal with CIP in general, as van Eijck and Unger [4] cannot.
So, in order to deal with CIP in general, we would like to introduce an interface between
DEL and focused pragmatic principles. As such an interface, by making use of PAL + Cs,h ,we propose a test of whether a presupposition is projected or not (Presupposition Projection
Test (PPT)). PPT gives a solution to Problem 2. （使用言語：日本語）

参考文献[1] Baltag, A., Renne, B.: Dynamic epistemic logic (winter 2016 edition) (2016), Stanford Encyclopedia of Philosophy[2] Baltag, A.e.a.: The logic of announcements, common knowledge, and private suspicions. In:Gilboa, I. (ed.) The Proceedings of TARK VII. pp. 43–56 (1998)[3] Beaver, D.I.e.a.: Presupposition (spring 2021 edition) (2021), Stanford Encyclopedia of Philosophy[4] van Eijck, J., Unger, C.: The epistemics of presupposition projection. In: Aloni, M.e.a. (ed.)
Proceedings of the Sixteenth Amsterdam Colloquium. pp. 235–240 (2007)[5] Heim, I.: On the projection problem for presuppositions. In: Barlow, M.e.a. (ed.) WCCFL 2. pp.
114–125 (1983)[6] Rothschild, D., Yalcin, S.: Three notions of dynamicness in language. Linguistics and Philosophy
39, 333–355 (2016)[7] Soames, S.: Presupposition. In: Handbook of Philosophical Logic 4, pp. 553–616 (1989)[8] Stalnaker, R.C.: Presuppositions. Journal of Philosophical Logic 2, 447–457 (1973)

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