The Broadest Necessity

In this paper the logic of broad necessity is explored. Definitions of what it means for one modality to be broader than another are formulated, and it is proven, in the context of higher-order logic, that there is a broadest necessity, settling one of the central questions of this investigation. It is shown, moreover, that it is possible to give a reductive analysis of this necessity in extensional language. This relates more generally to a conjecture that it is not possible to define intensional connectives from extensional notions. This conjecture is formulated precisely in higher-order logic, and concrete cases in which it fails are examined. The paper ends with a discussion of the logic of broad necessity. It is shown that the logic of broad necessity is a normal modal logic between S4 and Triv, and that it is consistent with a natural axiomatic system of higher-order logic that it is exactly S4. Some philosophical reasons to think that the logic of broad necessity does not include the S5 principle are given

Complete Additivity and Modal Incompleteness

In this paper, we tell a story about incompleteness in modal logic. The story weaves together a paper of van Benthem, `Syntactic aspects of modal incompleteness theorems,' and a longstanding open question: whether every normal modal logic can be characterized by a class of completely additive modal algebras, or as we call them, V-BAOs. Using a first-order reformulation of the property of complete additivity, we prove that the modal logic that starred in van Benthem's paper resolves the open question in the negative. In addition, for the case of bimodal logic, we show that there is a naturally occurring logic that is incomplete with respect to V-BAOs, namely the provability logic GLB. We also show that even logics that are unsound with respect to such algebras do not have to be more complex than the classical propositional calculus. On the other hand, we observe that it is undecidable whether a syntactically defined logic is V-complete. After these results, we generalize the Blok Dichotomy to degrees of V-incompleteness. In the end, we return to van Benthem's theme of syntactic aspects of modal incompleteness

Phrasal and Clausal Exceptive-Additive Constructions Crosslinguistically

This work focuses on the syntax and semantics of exceptive and exceptive-additive constructions across different languages. Exceptive-additive constructions are constructions that can be interpreted as ‘except for’ and ‘in addition to’ depending on the context they are used in. The meaning an exceptive-additive construction gets depends on the other functional elements in a sentence. Those constructions get the exceptive meaning when they are put together with universal quantifiers and they get the additive meaning with existentials, wh-words and focus associates. In each context only one of the meanings is available. This work is the first systematic study of the syntactic and semantic properties of such constructions across serval languages: English, Russian, Turkish, Hindi, Persian, Bulgarian. This works offers a formal theory that explains how exceptive-additive constructions can mean two different things and why are the two readings distributed the way they are. According to this proposal, the meaning of an exceptive-additive construction is contributed by two operators that can take scope with respect to each other. Their scope determines the resulting meaning. In every case both the additive and the exceptive meaning are generated. However, an attempt to generate the additive meaning with a universal quantifier or the exceptive meaning with a wh-question results in a meaning that is ill-formed and for that reason is not available. This work also adds novel observations supporting the claim that the syntactic structure the standard semantic theory of exceptives assumes is incorrect for some exceptive constructions. In many languages what follows the word except is a reduced clause and not a DP. This work proposes the first compositional semantic treatment of clausal exceptives. According to this proposal a clausal exceptive contributes quantification over possible situations and provides the restriction for this quantification. The proposed account captures the known inferences exceptives contribute and the restrictions on their use. This work also describes clausal exceptive-additive constructions in Persian and Bulgarian and extends the account of the exceptive-additive ambiguity to clausal cases. Key words: exceptive constructions, clausal exceptives, phrasal exceptives, exceptive-additive ambiguit

Proof Theory of Finite-valued Logics

The proof theory of many-valued systems has not been investigated to an extent comparable to the work done on axiomatizatbility of many-valued logics. Proof theory requires appropriate formalisms, such as sequent calculus, natural deduction, and tableaux for classical (and intuitionistic) logic. One particular method for systematically obtaining calculi for all finite-valued logics was invented independently by several researchers, with slight variations in design and presentation. The main aim of this report is to develop the proof theory of finite-valued first order logics in a general way, and to present some of the more important results in this area. In Systems covered are the resolution calculus, sequent calculus, tableaux, and natural deduction. This report is actually a template, from which all results can be specialized to particular logics

Situations and individuals

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Linguistics and Philosophy, 2002.Includes bibliographical references (p. 220-233).I argue that definite descriptions, pronouns and proper names share one common syntax and semantics, basically that of definite descriptions. E-type pronouns are argued to be definite articles that take NP complements elided in the phonology; referential and bound variable pronouns are analyzed as definite articles taking indices as phonologically null complements. Proper names are shown to have previously undetected E-type and bound readings, meaning that they too are best regarded as definite descriptions. It is shown that this position has deleterious consequences for the philosophical theories of direct reference and rigid designation.by Paul Elbourne.Ph.D

The comparative

No idea is older in the history of linguistics than the thought that there is, somehow hidden underneath the surface of sentences, a form or a structure which provides a semantic analysis and lays bare their logical structure. In Plato’s Cratylus the theory was proposed, deriving from Heraclitus’ theory of explanatory underlying structure in physical nature, that words contain within themselves bits of syntactic structure giving their meanings. The Stoics held the same view and maintained moreover that every sentence has an underlying logical structure, which for them was the Aristotelian subject- predicate form. They even proposed transformational processes to derive the surface from the deep structure. The idea of a semantically analytic logical form underlying the sentences of every language kept reappearing in various guises at various times. Quite recently it re-emerged under the name of generative semantics

On the Logic of Belief and Propositional Quantification

We consider extending the modal logic KD45, commonly taken as the baseline system for belief, with propositional quantifiers that can be used to formalize natural language sentences such as “everything I believe is true” or “there is some-thing that I neither believe nor disbelieve.” Our main results are axiomatizations of the logics with propositional quantifiers of natural classes of complete Boolean algebras with an operator (BAOs) validating KD45. Among them is the class of complete, atomic, and completely multiplicative BAOs validating KD45. Hence, by duality, we also cover the usual method of adding propositional quantifiers to normal modal logics by considering their classes of Kripke frames. In addition, we obtain decidability for all the concrete logics we discuss

Supervenience, Dependence, Disjunction

This paper explores variations on and connections between the topics mentioned in its title, using as something of an anchor the discussion in Valentin Goranko and Antti Kuusisto’s “Logics for propositional determinacy and independence”, a venture into what the authors call the logic of determinacy, which they contrast with (a demodalized version of) Jouko Väänänen’s modal dependence logic. As they make clear in their discussion, these logics are closely connected with the topics of noncontingency and supervenience. Two opening sections of the present paper address some of these connections, including related earlier logical work by the present author as well as very recent work by Jie Fan. The Väänänen-inspired treatment is presented in a third section, and then, in Sections 4 and 5, as a kind of centerpiece for the discussion, we follow Goranko and Kuusisto in elaborating one principal reason offered for preferring their own approach over that treatment, which concerns some anomalies over the behaviour of disjunction in the latter treatment. Sections 6 and 7 look at dependence and (several different versions of) disjunction in inquisitive logic, especially as presented by Ivano Ciardelli. Section 8 revisits the less formal property-supervenience literature with issues from the first two sections of the paper in mind, and we conclude with a Postscript addressing a further conceptual issue pertaining to the relation between modal and quantificational dependence logics

THE SEMANTICS OF PROPER NAMES AND OTHER BARE NOMINALS

This research proposes a unified approach to the semantics of the so-called bare nominals, which include proper names (e.g., `Mary'), mass and plural terms (e.g., `water', `cats'), and articleless noun phrases in Japanese. I argue that bare nominals themselves are monadic predicates applicable to more than one particular, but they can constitute complex referential phrases when located within an appropriate linguistic environment. Bare nominals used as the subjects or objects of sentences are some or other variant of definite descriptions, which are analyzed as non-quantificational, referential expressions. The overarching thesis is that the semantic properties of bare nominal expressions such as rigidity are not inherent in the words themselves, but derived from the basic features of complex nominal phrases