Connectives, Misc

This paper surveys the common approach to quantification and generalised quantification in formal linguistics and philosophy of language. We point out how this general setting departs from empirical linguistic data, and give some hints for a different view based on proof theory, which on many aspects gets closer to the language itself. We stress the importance of Hilbert's oper- ator epsilon and tau for, respectively, existential and universal quantifications. Indeed, these operators help a lot to construct semantic representation close to (...) natural language, in particular with quantified noun phrases as individual terms. We also define guidelines for the design of the proof rules corresponding to generalised quantifiers. (shrink)

У статті проаналізовано синкретичні семантико-синтаксичні відношення у структурі складнопідрядних займенниково-співвідносних речень симетричного типу, з’ясовано причини, що впливають на формування цих синкретичних відношень.

A problem is raised for the introduction rules proposed in Benjamin Schnieder’s ‘A logic for “because”’, arising in connection with (a) inferences that the rules should not, but do, validate and (b) inferences that the rules should, but do not, validate.

Fara and Williamson (Mind, 2005) argue that counterpart theory is unable to account for modal claims that use an actuality operator. This paper argues otherwise. Rather than provide a different counterpart translation of the actuality operator itself, the solution presented here starts out with a quantified modal logic in which the actuality operator is redundant, and then translates the sentences of this logic into claims of counterpart theory.

We explore the technical details and historical evolution of Charles Peirce's articulation of a truth table in 1893, against the background of his investigation into the truth-functional analysis of propositions involving implication. In 1997, John Shosky discovered, on the verso of a page of the typed transcript of Bertrand Russell's 1912 lecture on ?The Philosophy of Logical Atomism? truth table matrices. The matrix for negation is Russell's, alongside of which is the matrix for material implication in the hand of Ludwig (...) Wittgenstein. It is shown that an unpublished manuscript identified as composed by Peirce in 1893 includes a truth table matrix that is equivalent to the matrix for material implication discovered by John Shosky. An unpublished manuscript by Peirce identified as having been composed in 1883?1884 in connection with the composition of Peirce's ?On the Algebra of Logic: A Contribution to the Philosophy of Notation? that appeared in the American Journal of Mathematics in 1885 includes an example of an indirect truth table for the conditional. (shrink)

There are certain uses of and and or that cannot be explained by their normal meanings as truth-functional connectives, even with sophisticated pragmatic resources. These include examples such as The cops show up, and a fight will break out (‘If the cops show up, a fight will break out’), and I have no friends, or I would throw a party (‘I have no friends. If I did have friends, I would throw a party.’). We argue that these uses are indeed (...) distinct from the more ordinary uses of and and or, but that they are nonetheless related in a principled way. To explain them we give an analysis of what we call the dynamic effects of connectives, which arise in all their uses. The special uses at issue are then argued to be instances where the connectives exhibit their dynamic effects without their truth-conditional meaning. (shrink)

This paper focuses on the interpretation of the Italian approximative adverb quasi 'almost' by primarily looking at cases in which it modifies temporal connectives, a domain which, to our knowledge, has been largely unexplored thus far. Consideration of this domain supports the need for a scalar account of the semantics of quasi (close in spirit to Hitzeman's semantic analysis of almost, in: Canakis et al. (eds) Papers from the 28th regional meeting of the Chicago Linguistic Society, 1992). When paired with (...) suitable analyses of temporal connectives, such an account can provide a simple explanation of the patterns of implication that are observed when quasi modifies locational (e. g. quando 'when'), directional (e. g. fino 'until' and da 'since'), and event-sequencing temporal connectives (e. g. prima 'before' and dopo ' after'). A challenging empirical phenomenon that is observed is a contrast between the modification of fino and da by quasi, on the one hand, and the modification of prima and dopo by the same adverb, on the other. While quasi fino and quasi da behave symmetrically, a puzzling asymmetry is observed between quasi prima and quasi dopo. To explain the asymmetry, we propose an analysis of prima and dopo on which the former has the meaning of the temporal comparative più presto 'earlier', while the latter is seen as an atomic predicate denoting temporal succession between events (Del Prete, Nat Lang Semantics 16: 157-203, 2008). We show that the same pattern of implication observed for quasi prima is attested when quasi modifies overt comparatives, and propose a pragmatic analysis of this pattern that uniformly applies to both cases, thus providing new evidence for the claim that prima is underlyingly a comparative. A major point of this paper is a discussion of the notion of scale which is relevant for the semantics of quasi', in particular, we show that the notion of Horn (entailment-based) scale is not well-suited for handling modification of temporal connectives, and that a more general notion of scale is required in order to provide a uniform analysis of quasi as a cross-categorial modifier. (shrink)

This is a study in the meaning of natural language probability operators, sentential operators such as probably and likely. We ask what sort of formal structure is required to model the logic and semantics of these operators. Along the way we investigate their deep connections to indicative conditionals and epistemic modals, probe their scalar structure, observe their sensitivity to contex- tually salient contrasts, and explore some of their scopal idiosyncrasies.

This paper sets forth a new theory of quantifiers and term connectives, called shadow theory , which should help simplify various semantic theories of natural language by greatly reducing the need of Montagovian proper names, type-shifting, and λ-conversion. According to shadow theory, conjunctive, disjunctive, and negative noun phrases such as John and Mary , John or Mary , and not both John and Mary , as well as determiner phrases such as every man , some woman , and the boys (...) , are all of semantic type e and denote individual-like objects, called shadows — conjunctive , disjunctive , or negative shadows, such as John-and-Mary, John-or-Mary, and not-(John-and-Mary). There is no essential difference between quantification and denotation: quantification is nothing but denotation of shadows. Individuals and shadows constitute a Boolean structure. Formal language LSD (Language for Shadows with Distributivity), which takes compound terms to denote shadows, is investigated. Expansions and enrichments of LSD are also considered toward the end of the paper. (shrink)

Polarized unification grammar (PUG) is a linguistic formalism which uses polarities to better control the way grammar fragments interact. The grammar combination operation of PUG was conjectured to be associative. We show that PUG grammar combination is not associative, and even attaching polarities to objects does not make it order-independent. Moreover, we prove that no non-trivial polarity system exists for which grammar combination is associative. We then redefine the grammar combination operator, moving to the powerset domain, in a way that (...) guarantees associativity. The method we propose is general and is applicable to a variety of tree-based grammar formalisms. (shrink)

In this paper, I argue that the temporal connective prima (‘before’) is a comparative adverb. The argument is based on a number of grammatical facts from Italian, showing that there is an asymmetry between prima and dopo (‘after’). On the ground of their divergent behaviour, I suggest that dopo has a different grammatical status from prima. I propose a semantic treatment for prima that is based on an independently motivated analysis of comparatives which can be traced back to Seuren (in: (...) Kiefer and Ruwet (eds.) Generative grammar in Europe, 1973). Dopo is analyzed instead as an atomic two-place predicate which contributes a binary relation over events to the sentence meaning. The different semantic treatments of the two connectives provide an explanation for the grammatical asymmetries considered at the outset; interestingly, they also shed some light on other asymmetries between prima and dopo, which are known to hold for the English temporal connectives before and after as well: these asymmetries are related to the veridicality properties, the distribution of NPIs, and the logical properties of these connectives first described in Anscombe (Philos Rev 73:3–24, 1964). (shrink)

Metalinguistic operations signify understanding and translation, specified in Jakobson’s varieties of six language functions and his three types of translation. Both models were first presented in the 1950s. This article is rooted in Jakobson’s models in connection with Peirce’s three categories. Bühler’s three functions with qualitative difference anticipated, perhaps not accidentally, Jakobson’s distinctions indicating qualitative difference within literary forms and structures as well as other fine arts. The semiotic discovery, criticism and perspective of elements and code-units settle the numerical differences (...) as well as the differences in realistic messages and conceptual codes. Jakobson’s intersemiotic translation is updated in vocal translation, which deals with the virtual reality of opera on stage, reaching a catharsis of the operatic mystique. The word-tone synthesis of opera (or semiosic symbiosis) will demonstrate the typological unification of verbal and nonverbal languages. (shrink)

C I Lewis showed up Down Under in 2005, in e-mails initiated by Allen Hazen of Melbourne. Their topic was the system Hazen called FL (a Funny Logic), axiomatized in passing in Lewis 1921. I show that FL is the system MEN of material equivalence with negation. But negation plays no special role in MEN. Symbolizing equivalence with → and defining ∼A inferentially as A→f, the theorems of MEN are just those of the underlying theory ME of pure material equivalence. (...) This accords with the treatment of negation in the Abelian l-group logic A of Meyer and Slaney (Abelian logic. Abstract, Journal of Symbolic Logic 46, 425–426, 1981), which also defines ∼A inferentially with no special conditions on f. The paper then concentrates on the pure implicational part AI of A, the simple logic of Abelian groups. The integers Z were known to be characteristic for AI, with every non-theorem B refutable mod some Zn for finite n. Noted here is that AI is pre-tabular, having the Scroggs property that every proper extension SI of AI, closed under substitution and detachment, has some finite Zn as its characteristic matrix. In particular FL is the extension for which n = 2 (Lewis, The structure of logic and its relation to other systems. The Journal of Philosophy 18, 505–516, 1921; Meyer and Slaney, Abelian logic. Abstract. Journal of Symbolic Logic 46, 425–426, 1981; This is an abstract of the much longer paper finally published in 1989 in G. G. Priest, R. Routley and J. Norman, eds., Paraconsistent logic: essays on the inconsistent, Philosophica Verlag, Munich, pp. 245–288, 1989). (shrink)

Two experiments were conducted to show that the IF … THEN … rules used in the different versions of Wason 's selection task are not psychologically—though they are logically—equivalent. Some of these rules are considered by the participants as strict logical conditionals, whereas others are interpreted as expressing a biconditional relationship. A deductive task was used jointly with the selection task to show that the original abstract rule is quite ambiguous in this respect, contrary to deontic rules: the typical “error” (...) made by most people may indeed be explained by the fact that they consider the abstract rule as a biconditional. Thus, there is no proper error or bias in the selection task as it is still argued, but a differential interpretation of the rule. The need for taking into account a pragmatic component in the process of reasoning is illustrated by the experiments. (shrink)

It was shown in the previous work of the author that one can avoid the paradox of minimal logic { ϕ , ¬ ϕ } ¬ ψ defining the negation operator via reduction not a constant of absurdity, but to a unary operator of absurdity. In the present article we study in details what does it mean that negation in a logical system can be represented via an absurdity or contradiction operator. We distinguish different sorts of such presentations. Finally, we (...) consider the possibility to represent the negation via absurdity and contradiction operators in such well known systems of paraconsistent logic as D.Batens's logic CLuN and Sette's logic P 1. (shrink)

In introductory logic courses the authors often limit their considerations to the truth-value operators. Then they write that conditionals and biconditionals of natural language ("if" and "if and only if") may be represented as material implications and equivalences ("⊃" and "≡"), respectively. Yet material implications are not suitable for conditionals. Lewis' strict implications are much better for this purpose. Similarly, strict equivalences are better for representing biconditionals (than material equivalences). In this paper we prove that the methods from standard first (...) courses in logic can be used for testing arguments with strict implications, strict equivalences and other operators which may represent connectives from natural language. (shrink)

Solves what is sometimes, but not always, referred to as the third paradox of material implication. Readers downloading this piece should please also download the corrigendum. Note that "pragmatic" is here used in its original sense of context-sensitive, that is, adjacency. (This comment is made in response to an article in a student journal published in the western U.S. which claimed that I said that because something involves translation it must be pragmatic; that is so, in the original sense; only (...) grammaticality can ever be context-free; all meaning is context-sensitive, as "lawful" cannot meaningfully modify "whale."). (shrink)

In this paper the language of first-order modal logic is enriched with an operator @ ('actually') such that, in any model, the evaluation of a formula @A at a possible world depends on the evaluation of A at the actual world. The models have world-variable domains. All the logics that are discussed extend the classical predicate calculus, with or without identity, and conform to the philosophical principle known as serious actualism. The basic logic relies on the system K, whereas others (...) correspond to various properties that the actual world may have. All the logics are axiomatized. (shrink)

In the first part of this article, we show that, contrary to the Gricean tradition, inter-clausal and is not semantically equivalent to logical conjunction and, contrary to temporal approaches such as Bar-Levand Palacas 1980, it is not temporallyloaded. We then explore a commonsenseidea – namely that while sentence juxtaposition might be interpreted either as discourse coordination or subordination, and indicates coordination. SDRT already includes notions of coordinating and subordinating discourse relations (cf. Lascarides and Asher 1993, Asher 1993), and the meaning (...) of and is related to this distinction. Similar distinctions that play a crucial role in anaphora resolution have also appeared in AI – cf. Scha and Polanyi 1988, or Webber 1991. However, this discourse-structure-based distinction has not been well defined yet, and our approach provides independent motivation for it. This paper argues that the semantics of and includes a notion of coordination expressed as the requirement of a Coordinated Discourse Topic (CDT).CDT characterizes aclass of discourse relations, among which are Narration and Result.Once the basic semanticcontribution of and is isolated, effects related to its presence such as changes in temporal structure, blocking of a Discourse Relation, or conditional meanings are shown to follow from the defeasiblearchitecture set up by SDRT. (shrink)

In this note we show that the classical modal technology of Sahlqvist formulas gives quick proofs of the completeness theorems in [8] (D. Gregory, Completeness and decidability results for some propositional modal logics containing "actually" operators, Journal of Philosophical Logic 30(1): 57-78, 2001) and vastly generalizes them. Moreover, as a corollary, interpolation theorems for the logics considered in [8] are obtained. We then compare Gregory's modal language enriched with an "actually" operator with the work of Arthur Prior now known under (...) the name of hybrid logic. This analysis relates the "actually" axioms to standard hybrid axioms, yields the decidability results in [8], and provides a number of complexity results. Finally, we use a bisimulation argument to show that the hybrid language is strictly more expressive than Gregory's language. (shrink)

I present an analysis of Free Choice Items (FCIs), based on Scandinavian, where FCIs are complex and distinct from polarity sensitive items. Scandinavian FCIs are argued to have two components. One is a universal quantifying into modal contexts. The other is an operator mapping a type (s,t) expression onto itself, adjoining to the closest type t or (s,t) expression. Thus invoking Intensional Functional Application, this operator requires the presence of a modal in the scope of the universal quantifier. Facts concerning (...) ‘essential connections’ and ‘existential import’ are accounted for by assuming that the FC determiner has the option of acting like a quantifier. (shrink)

We put forth a theory of conditional elements which can be used to dismiss apparent challenges to the truth-functionality of the conditional without apparent circularity. In the process, we refine the ideas of Yoes, published in an earlier paper in this journal, broadening and deepening them.

This paper aims to provide a description of a metalinguistic use of simplement, one which occurs primarily in ce n'est pas que P simplement Q constructions. The two main points that will be raised concern the nature and function of the negation preceding P, and the meaning of simplement, which, following Anscombre and Ducrot, I will construe in procedural terms.

Proves two simple identities relating the biconditional and exclusive disjunction. -/- The PDF has been made available gratis by the publisher.

In [2] a semantics for implication is offered that makes use of stories — sets of sentences assembled under various constraints. Sentences are evaluated at an actual world and in each member of a set of stories. A sentence B is true in a story s just when B s. A implies B iff for all stories and the actual world, whenever A is true, B is true. In this article the first-order language of [2] is extended by the addition (...) of the operator the story... says that..., as in The story Flashman among the Redskins says that Flashman met Sitting Bull. The resulting language is shown to be sound and complete. (shrink)

The standard response is illustrated by E, J. Lemmon's claim that if all objects in a given universe had names and there were only finitely many of them, then we could always replace a universal proposition about that universe by a complex proposition. It is because these two requirements are not always met that we need universal quantification. This paper is partly in agreement with Lemmon and partly in disagreement. From the point of view of syntax and semantics we can (...) replace a universal proposition about any universe (finite or infinite, countable or uncountable) by a complex proposition (= sentence built up from atomic sentences and the connectives). But from the point of view of communication such a replacement is not possible if the universe is infinite. (shrink)

Let L be a sentential (object) language containing atoms ‘A’, ‘B’, . . . , and two logical connectives ‘&’ and ‘→’. In addition to these two logical connectives, L will also contain another binary connective ‘ ’, which is intended to be interpreted as the English indicative. In the meta-language for L , we will have two meta-linguistic operations: ‘ ’ and ‘ ’. ‘ ’ is a binary relation between individual sentences in L . It will be interpreted (...) as “single premise entailment” (or “single premise deducibility in L ”). ‘ ’ is a monadic predicate on sentences of L . It will be interpreted as “logical truth of the logic of L ” (or “theorem of the logic of L ”). We will not presuppose anything about the relationship between ‘ ’ and ‘ ’. Rather, we will state explicitly all assumptions about these meta-theoretic relations that will be required for Gibbard’s Theorem. (shrink)