Use-conditional meaning (original) (raw)

Towards a New Logic of Indicative Conditionals

In this paper I will propose a refinement of the semantics of hypervaluations (Mura 2009), one in which a hypervaluation is built up on the basis of a set of valuations, instead of a single val-uation. I shall define validity with respect to all the subsets of valua-tions. Focusing our attention on the set of valid sentences, it may easily shown that the rule substitution is restored and we may use valid schemas to represent classes of valid sentences sharing the same logical form. However, the resulting semantical theory TH turns out to be throughout a modal three-valued theory (modal sym-bols being definable in terms of the non modal connectives) and a fragment of it may be considered as a three-valued version of S5 system. Moreover, TH may be embedded in S5, in the sense that for every formula ϕ of TH there is a corresponding formula ϕ' of S5 such that ϕ' is S5-valid iff ϕ is TH-valid. The fundamental property of this system is that it allows the definition of a purely semantical relation of logical consequence which is coextensive to Adams’ p-entailment with respect to simple conditional sentences, without be-ing defined in probabilistic terms. However, probability may be well be defined on the lattice of hypervaluated tri-events, and it may be proved that Adam’s p-entailment, once extended to all tri-events, coincides with our notion of logical consequence as defined in purely semantical terms.

First-Order Conditional Logic and Neighborhood-Sheaf Semantics for Analysis of Conditional Sentences

New Frontiers in Artificial Intelligence (JSAI-isAI 2013 Workshops, LENLS, JURISIN, MiMI, AAA, and DDS, Kanagawa, Japan, October 27-28, 2013, Revised Selected Papers), Yukiko Nakano, Ken Satoh, Daisuke Bekki (Eds.), LNAI 8417, pp.154-164, Springer., 2014

Modals, conditionals and compositionality

Nijmegen: Radboud University Nijmegen thesis, 2008

Prologue xi 1 Note that I use the term 'modal expression' in a rather broad sense: any expression whose meaning depends on alternative states of affairs is a modal. In contrast, descriptive studies on modality, e.g. Coates (1983) and Palmer (2001), often reserve the term 'modal' for the class of such expressions that can be syntactically defined i.e. for the modal auxiliaries (these are set apart by the so-called NICE properties (Huddleston 1976)). Semi-auxiliaries like have to are then called 'semi-modals'. Arguably, my definition is too inclusive, whereas syntactic definitions are not inclusive enough, see Kiefer (1987), Narrog (2005), Zaefferer (2005) for definitional issues in the field of modality. 2 I adopt Kai von Fintel's strategy for alphabetizing last names like 'de Haan' that contain particles. That is, the article cited here will be alphabetized as 'de Haan, Ferdinand', but it will be listed under 'H'. See http://kaivonfintel.org/von/. Here the obligation is not put on the subject, but on the addressee. Apparently, the context of utterance determines who is the bearer of the obligation in (12). But if we need a pragmatic mechanism to identify the bearer for sentences like 8 The term 'root modality' seems to refer to root clauses (simple clauses that aren't contained in any other clause), but this is somewhat misleading, for root modals aren't restricted to such clauses, cf. de Haan (2005, 6). 9 This distinction between predicate and proposition operators of course corresponds to the distinction between control and raising verbs (Ross 1969, Perlmutter 1970, Jackendoff 1972, Brennan 1993). 10 To be sure, Bhatt and Wurmbrand argue that a predicate-level analysis of root modals is not only unnecessary, but also untenable. Their arguments come from case-marking in Hindi and Icelandic respectively. But as these arguments are quite intricate, I leave them out of the discussion, and refer the interested reader to the original papers instead. 11 The similarities between obligation and permission on the one hand and necessity and possibility on the other have been noted time and time again, at least since the 14 th century (Knuuttila 1981), and later by Leibniz (in Specimina juris (1667) and Elementa juris naturalis (1672), see Poser (1969)), and by von Wright, who writes that he independently made the discovery and was then prompted to write his Deontic logic (1951a), see von Wright (1999, 28). 12 Note though that these authors, as well as the authors they cite, only distinguish a subset of the modal meanings I have listed; most only distinguish epistemic and root meanings, where root modality comprises deontic and for some authors also dynamic modality. 15 Meredith & Prior (1956) seem to have been the first to employ a binary relation, and Hintikka (1957, 1961) was probably the first to explain this relation as relative possibility between conceivable states of affairs (possible worlds). Yet another pioneer of modal logic, Kanger (1957a,b), will remain famous for being the first who applied the semantics of quantified modal logic to philosophical problems such as the 'morning star paradox' (substitution of equals is not valid without restriction). See Goldblatt (2006) and Copeland (2002) for the history of relational semantics. 16 (Modal) sentential logic is commonly known as (modal) propositional logic, but I reserve the term 'proposition' strictly for the truth set or intension of formulas from the object language. See section 1.2.2 below for further explanation. 2 Material implication is sometimes attributed to Philo of Megara (4th century BC), but it was Frege who championed this semantics in modern logic. Russell happily took over this analysis and gave it its current name. For a historical overview of the battle concerning the right conditional semantics, see Kratzer (1978). 3 To be sure, the issue here is what truth value a conditional should have when its components are (true, true), (false, true), or (false, false). The argument presented here does not establish

Nominalizations: The Case of Nominalizations of Modal Predicates (Blackwell Companion to Semantics)

Nominalizations describing events and tropes have a received considerable interest in the semantic (and philosophical) literature. By contrast, nominalizations of modal predicates and the modal objects they describe have received little, if any, attention in the literature so far. This paper is a case study of nominalizations of the sort 'need', 'permission', 'obligation', 'ability', and 'possibility'. It argues that nominalizations of modal predicates require recognizing a novel ontological category of modal objects, entities that arguably play a role also in the semantics of modal sentences in general.

Non-normal modal logics and conditional logics: Semantic analysis and proof theory

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