Connectives

Simple taste predications come with an acquaintance requirement: they require the speaker to have had a certain kind of first-hand experience with the object of predication. For example, if I tell you that the creme caramel is delicious, you would ordinarily assume that I have actually tasted the creme caramel and am not simply relying on the testimony of others. The present essay argues in favor of a 'lightweight' expressivist account of the acquaintance requirement. This account consists of a recursive (...) semantics and an account of assertion; it is compatible with a number of different accounts of truth and content, including contextualism, relativism, and purer forms of expressivism. The principal argument in favor of this account is that it correctly predicts a wide range of data concerning how the acquaintance requirement interacts with Boolean connectives, generalized quantifiers, epistemic modals, and attitude verbs. (shrink)

This article focuses on `therefore' constructions such as ‘The switch is on, and therefore the lights are on’. We submit that the contribution of `therefore’ is to express a dependence as part of the core content of these constructions, rather than being conveyed by conventional implicature (Grice 1975, Potts 2005, Neta 2013) or a triggered presupposition (Pavese 2017, forthcoming, Stokke 2017). We argue that the standard objections to this view can be answered by relying on the general projection hypothesis defended (...) by Roberts et al. (2009) and Simons et al. (2010), leaving our view on solid ground. (shrink)

Conservation of a Circle is the core dynamic, and, therefore, the only 'constant' in Nature.

This paper develops a semantic solution to the puzzle of Free Choice permission. The paper begins with a battery of impossibility results showing that Free Choice is in tension with a variety of classical principles, including Disjunction Introduction and the Law of Excluded Middle. Most interestingly, Free Choice appears incompatible with a principle concerning the behavior of Free Choice under negation, Double Prohibition, which says that Mary can’t have soup or salad implies Mary can’t have soup and Mary can’t have (...) salad. Alonso-Ovalle 2006 and others have appealed to Double Prohibition to motivate pragmatic accounts of Free Choice. Aher 2012, Aloni 2018, and others have developed semantic accounts of Free Choice that also explain Double Prohibition. -/- This paper offers a new semantic analysis of Free Choice designed to handle the full range of impossibility results involved in Free Choice. The paper develops the hypothesis that Free Choice is a homogeneity effect. The claim possibly A or B is defined only when A and B are homogenous with respect to their modal status, either both possible or both impossible. Paired with a notion of entailment that is sensitive to definedness conditions, this theory validates Free Choice while retaining a wide variety of classical principles except for the transitivity of entailment. The homogeneity hypothesis is implemented in two different ways, homogeneous alternative semantics and homogeneous dynamic semantics, with interestingly different consequences. (shrink)

This paper offers an explanation of the fact that sentences of the form (1) ‘X may A or B’ may be construed as implying (2) ‘X may A and X may B’, especially if they are used to grant permission. It is suggested that the effect arises because disjunctions are conjunctive lists of epistemic possibilities. Consequently, if the modal may is itself epistemic, (1) comes out as equivalent to (2), due to general laws of epistemic logic. On the other hand, (...) on a deontic reading of may, (2) is only implied under exceptional circumstances – which usually obtain when (1) is used performatively. (shrink)

In this paper, we investigate the representation of negated sentences in Minimal Recursion Semantics (Copestake, Flickinger, Pollard, & Sag, 2005). We begin with its treatment in the English Resource Grammar (Flickinger, 2000, 2011), a broad-coverage implemented HPSG (Pollard & Sag, 1994), and argue that it is largely a suitable representation for English, despite possible objections. We then explore whether it is suitable for typologically different languages: namely, those that express sentential negation via inflection on the verb, particularly Turkish and Inuktitut. (...) We find that the interaction between negation and intersective modifiers requires a change to the way in which (at least) one of them contributes to semantic composition, and we argue for adapting the analysis of intersective modifiers. (shrink)

In the initial part of the article texts of some authors are analyzed concerning material implication. In the further part of the article the proposition is justified that the operator of material implication differs in quality from other truth-functional operators. The final part of the article is devoted to considerations aiming at presenting what the thesis of the classical propositional calculus, in which the main operator is the operator of material implication, denote.

In this paper, I explore the potential of systematically studying the linguistic surface of discourse for the purposes of identifying markers of argumentative moves and other related categories, such as types of arguments and argumentative strategies. Such a list of argumentative markers can prove useful for the (semi)automatic treatment of a large corpus of texts. After reviewing literature on the linguistic realization of argumentative moves as well as literature on the subject of discourse markers, it becomes clear that the search (...) for representative items of argumentative markers cannot be restricted to those elements marking relations but that it should also include elements that signal a certain function that is of pertinence to argumentative analysis. In this view, argumentative markers can be any single or complex lexical expression as well as a discursive configuration whose presence in a given utterance marks that utterance or the one preceding/following it, or a larger piece of discourse as having a certain argumentative function (as an argumentative move, a type of argument or an argumentative strategy). Examples taken from a French corpus on the controversy surrounding the development and applications of nanotechnology currently under study are used to illustrate the different types of argumentative markers proposed. (shrink)

(2) Peter wollte Potsdam nicht verlassen bevor das Projekt in ruhigem Fahrwasser war. There are other well-known examples of non-interpreted negation, viz. cases of so-called negative concord in Slavic and Romance languages, but also in dialects of German and English. But arguably, in those cases the “superfluous” negation has to be present for grammatical reasons, which is not the case here. I will show that the negation is in fact interpreted, and that, due to a complex interplay of semantic and (...) pragmatic factors, we do get truth conditions for the two sentences that are not quite identical, but very similar. (shrink)

Normative accounts in terms of similarity can be deployed in order to provide semantics for systems of context-free default rules and other sophisticated conditionals. In contrast, procedural accounts of decision in terms of similarity (Rubinstein 1997) are hard to reconcile with the normative rules of rationality used in decision-making, even when suitably weakened.

Grice’s distinction between what is said and what is implicated has greatly clarified our understanding of the boundary between semantics and pragmatics. Although border disputes still arise and there are certain difficulties with the distinction itself (see the end of §1), it is generally understood that what is said falls on the semantic side and what is implicated on the pragmatic side. But this applies only to what is..

We provide a semantic analysis of respective readings, including butnot limited to the interpretation of examples containing the adverbrespectively, which accounts for a number of facts that haveeither proven difficult for previous studies or heretofore goneunnoticed in the literature. The analysis introduces the new notionsof property sum and proposition sum which integrate smoothly with existing analyses of plurals and distributivity. The analysis also admits of a straightforward account of previouslyunacknowledged examples involving filler-gap dependencies that areproblematic for contemporary syntactic theories. Ramifications (...) anddirections for future research are discussed. (shrink)

We consider the variety of Dynamic Relation Algebras V(DRA). We show that the monoid of an algebra in this variety determines dynamic negation uniquely.

It will be an essential resource for philosophers, mathematicians, computer scientists, linguists, or any scholar who finds connectives, and the conceptual issues surrounding them, to be a source of interest.This landmark work offers both ...

A formal, computational, semantically clean representation of natural language is presented. This representation captures the fact that logical inferences in natural language crucially depend on the semantic relation of entailment between sentential constituents such as determiner, noun, adjective, adverb, preposition, and verb phrases.The representation parallels natural language in that it accounts for human intuition about entailment of sentences, it preserves its structure, it reflects the semantics of different syntactic categories, it simulates conjunction, disjunction, and negation in natural language by computable (...) operations with provable mathematical properties, and it allows one to represent coordination on different syntactic levels. (shrink)

We attempt to define the classical propositional logic by use of appropriate derivability conditions called Cn-definitions. The conditions characterize basic properties of propositional connectives.

This paper uses the strengthened liar paradox as a springboard to illuminate two more general topics: i) the negation operator and the speech act of denial among speakers of English and ii) some ways the potential for acceptable language change is constrained by linguistic meaning. The general and special problems interact in reciprocally illuminating ways. The ultimate objective of the paper is, however, less to solve certain problems than to create others, by illustrating how the issues that form the topic (...) of this paper are more intricate than previously realised, and that they are related in delicate and somewhat surprising ways. (shrink)

A general mathematical framework, based on countable partitions of Natural Numbers [1], is presented, that allows to provide a Semantics to propositional languages. It has the particularity of allowing both the valuations and the interpretation Sets for the connectives to discriminate complexity of the formulas. This allows different adequacy criteria to be used to assess formulas associated with the same connective, but that differ in their complexity. The presented method can be adapted potentially infinite number of connectives and truth values, (...) therefore, it can be considered a general framework to provide semantics to several of the known logic systems (eg, LC, L3 LP, FDE). The presented semantics allow to converge to different standard semantics if the separation complexity procedure is annulled. Therefore, it can be understood as a framework that allows greater precision (in complexity terms) with respect to formula satisfaction. Naturally, because of how it is built, it can be incorporated into non-deterministic semantics. The presented procedure also allows generating valuations that grant a different truth value to each formula of propositional language. As a positive side effect, our method allows a constructive proof of the equipotence between N and N^n for all Natural n. (shrink)

In recent years, there has been a growing interest in truthmaker semantics as a framework for understanding a range of phenomena in philosophy and linguistics. Despite this interest, there has been limited study of the various logics that arise from the semantics. This paper aims to address this gap by exploring numerous ‘truthmaker logics’ and proving their compactness and decidability. This is in continuation with the inquiry of Fine and Jago (2019), who proved compactness and decidability for a particular kind (...) of truthmaker logic. The key results going into this are (1) ‘standard translations’ into first-order logic; (2) a truthmaker analogue of the finite model property; and (3) a proof showing that truthmaker consequence on semilattices coincides with truthmaker consequence on complete lattices. Finally, the connection with modal logic is examined. Specifically, it is illustrated how endowing truthmaker semantics with classical negation results in modal information logics. (shrink)

According to perspectival realism, reality is (at least partially) constituted by “purely perspectival” facts, that is, facts that appear to describe reality only from a given “perspective”. Fragmentalism is a form of perspectival realism that maintains both that no perspective is privileged and that perspectival facts constitute reality absolutely. Assuming that reality is sufficiently variegated, fragmentalism entails that reality is absolutely constituted by incompatible facts. Given that incompatible facts can never obtain together, reality must be divided into a plurality of (...) “fragments” that never compose a coherent, unitary whole. The main aim of this paper is to provide the first rigorous, detailed map of fragmentalism and its rivals. First, we will argue that fragmentalism is best construed as having two “unitist” (that is, non-fragmentalist) boundaries, which we will call ‘coherent’ and ‘incoherent unitism’. Second, we will present what we take to be the six main viable versions of fragmentalism and show how they can be categorized according to whether they take the logical operations of conjunction and negation to be either “local” or “global”. (shrink)

Fragmentalism allows incompatible facts to constitute reality in an absolute manner, provided that they fail to obtain together. In recent years, the view has been extensively discussed, with a focus on its formalisation in model-theoretic terms. This paper focuses on three formalisations: Lipman’s approach, the subvaluationist interpretation, and a novel view that has been so far overlooked. The aim of the paper is to explore the application of these formalisations to the alethic modal case. This logical exploration will allow us (...) to study (i) cases of metaphysical incompatibility between modal facts and (ii) cases of modal dialetheias. In turn, this will enrich our understanding of the role of impossibility in the fragmentalist framework. (shrink)

Logical connectives (otherwise known as 'logical constants' or 'logical particles') have seemed challenging to philosophers of language. This article gives a concise account of logical connectives.

We give a proof-theoretic as well as a semantic characterization of a logic in the signature with conjunction, disjunction, negation, and the universal and existential quantifiers that we suggest has a certain fundamental status. We present a Fitch-style natural deduction system for the logic that contains only the introduction and elimination rules for the logical constants. From this starting point, if one adds the rule that Fitch called Reiteration, one obtains a proof system for intuitionistic logic in the given signature; (...) if instead of adding Reiteration, one adds the rule of Reductio ad Absurdum, one obtains a proof system for orthologic; by adding both Reiteration and Reductio, one obtains a proof system for classical logic. Arguably neither Reiteration nor Reductio is as intimately related to the meaning of the connectives as the introduction and elimination rules are, so the base logic we identify serves as a more fundamental starting point and common ground between proponents of intuitionistic logic, orthologic, and classical logic. The algebraic semantics for the logic we motivate proof-theoretically is based on bounded lattices equipped with what has been called a weak pseudocomplementation. We show that such lattice expansions are representable using a set together with a reflexive binary relation satisfying a simple first-order condition, which yields an elegant relational semantics for the logic. This builds on our previous study of representations of lattices with negations, which we extend and specialize for several types of negation in addition to weak pseudocomplementation; in an appendix, we further extend this representation to lattices with implications. Finally, we discuss adding to our logic a conditional obeying only introduction and elimination rules, interpreted as a modality using a family of accessibility relations. (shrink)

In this paper, we study three representations of lattices by means of a set with a binary relation of compatibility in the tradition of Ploščica. The standard representations of complete ortholattices and complete perfect Heyting algebras drop out as special cases of the first representation, while the second covers arbitrary complete lattices, as well as complete lattices equipped with a negation we call a protocomplementation. The third topological representation is a variant of that of Craig, Haviar, and Priestley. We then (...) extend each of the three representations to lattices with a multiplicative unary modality; the representing structures, like so-called graph-based frames, add a second relation of accessibility interacting with compatibility. The three representations generalize possibility semantics for classical modal logics to non-classical modal logics, motivated by a recent application of modal orthologic to natural language semantics. (shrink)

In this paper, we will motivate the application of specific rules of inference from the propositional calculus to natural language sentences. Specifically, we will analyse De Morgan’s laws, which pertain to the interaction of two central topics in syntactic research: negation and coordination. We will argue that the applicability of De Morgan’s laws to natural language structures can be derived from independently motivated operations of grammar and principles restricting the application of these operations. This has direct empirical consequences for the (...) hypothesised relations between natural language and logic. (shrink)

Import-Export says that a conditional 'If p, if q, r' is always equivalent to the conditional 'If p and q, r'. I argue that Import-Export does not sit well with a classical approach to conjunction: given some plausible and widely accepted principles about conditionals, Import-Export together with classical conjunction leads to absurd consequences. My main goal is to draw out these surprising connections. In concluding I argue that the right response is to reject Import-Export and adopt instead a limited version (...) which better fits natural language data; accounts for all the intuitions that motivate Import-Export in the first place; and fits better with a classical conjunction. (shrink)

Is the mechanism behind presupposition projection and filtering fundamentally asymmetric or symmetric? This is a foundational question for the theory of presupposition which has been at the centre of attention in recent literature :287–316, 2008b. https://doi.org/10.1515/THLI.2008.021, Semant Pragmat 2:1–78, 2009. https://doi.org/10.3765/sp.2.3; Rothschild in Semant Pragmat 4:1–43, 2011/2015. https://doi.org/10.3765/sp.4.3 a.o.). It also bears on broader issues concerning the source of asymmetries observed in natural language: are these simply rooted in superficial asymmetries of language use ; or are they, at least in (...) part, directly encoded in linguistic knowledge and representations? In this paper we aim to make progress on these questions by exploring presupposition projection across conjunction, which has traditionally been taken as a central piece of evidence that presupposition filtering is asymmetric in general. As a number of authors have recently pointed out, however, the evidence which has typically been used to support this conclusion is muddied by independent issues concerning redundancy; additional concerns have to do with the possibility of local accommodation. We report on a series of experiments, building on previous work by Chemla and Schlenker :177–226, 2012. https://doi.org/10.1007/s11050-012-9080-7) and Schwarz Experimental perspectives on presuppositions, Springer, Cham, 2015), using inference and acceptability tasks, which aim to control for both of these potential confounds. In our results, we find strong evidence for left-to-right filtering across conjunctions, but no evidence for right-to-left filtering—even when right-to-left filtering would, if available, rescue an otherwise unacceptable sentence. These results suggest that presupposition filtering across conjunction is asymmetric, contra suggestions in the recent literature :157–212, 2008a. https://doi.org/10.1515/THLI.2008.013, 2009 a.o.), and pave the way for the investigation of further questions about the nature of this asymmetry and presupposition projection more generally. Our results also have broader implications for the study of presupposition: we find important differences in the verdicts of acceptability versus inference tasks in testing for projected content, which has both methodological ramifications for the question of how to distinguish presupposed content, and theoretical repercussions for understanding the nature of projection and presuppositions more generally. (shrink)

This paper extends Fitting's epistemic interpretation of some Kleene logics, to also account for Paraconsistent Weak Kleene logic. To achieve this goal, a dualization of Fitting's "cut-down" operator is discussed, rendering a "track-down" operator later used to represent the idea that no consistent opinion can arise from a set including an inconsistent opinion. It is shown that, if some reasonable assumptions are made, the truth-functions of Paraconsistent Weak Kleene coincide with certain operations defined in this track-down fashion. Finally, further reflections (...) on conjunction and disjunction in the weak Kleene logics accompany this paper, particularly concerning their relation with containment logics. These considerations motivate a special approach to defining sound and complete Gentzen-style sequent calculi for some of their four-valued generalizations. (shrink)

In this paper we discuss the extent to which conjunction and disjunction can be rightfully regarded as such, in the context of infectious logics. Infectious logics are peculiar many-valued logics whose underlying algebra has an absorbing or infectious element, which is assigned to a compound formula whenever it is assigned to one of its components. To discuss these matters, we review the philosophical motivations for infectious logics due to Bochvar, Halldén, Fitting, Ferguson and Beall, noticing that none of them discusses (...) our main question. This is why we finally turn to the analysis of the truth-conditions for conjunction and disjunction in infectious logics, employing the framework of plurivalent logics, as discussed by Priest. In doing so, we arrive at the interesting conclusion that —in the context of infectious logics— conjunction is conjunction, whereas disjunction is not disjunction. (shrink)

Plurality, Conjunction and Events presents a novel theory of plural and conjoined phrases, in an event-based semantic framework. It begins by reviewing options for treating the alternation between `collective' and `distributive' readings of sentences containing plural or conjoined noun phrases, including analyses from both the modern and the premodern literature. It is argued that plural and conjoined noun phrases are unambiguously group-denoting, and that the collective/distributive distinction therefore must be located in the predicates with which these noun phrases combine. More (...) specifically, predicates must have a hidden argument place for events; the collective/distributive distinction may then be represented in the part/whole structure of these events. This allows a natural treatment of `collectivizing' adverbial expressions, and of `pluractional' affixes; it also allows a unified semantics for conjunction, in which conjoined sentences and predicates denote groups of events, much like conjoined noun phrases denote groups of individuals. (shrink)

Most philosophers seem to be under a misleading impression about the difference between ‘and’ and ‘but’. They hold that they are truth-functional equivalents but that ‘but’ adds a Gricean ‘conventional implicature’ to ‘and’. Frege thought that the implicature attached to ‘but’ was that the second clause is unlikely given the first; others have simply said they express a contrast between the two. Though the second formulation may seem more general, in practice writers seem to agree with Frege's idea. The present (...) note will argue against this conventional view. Indeed, ‘and’ and ‘but’ may both convey conflicting implicatures; and the traditional characterization of the implicature of ‘but’ is outright mistaken, or at least misleading. (shrink)

The central topic of this inquiry is a cross-linguistic contrast in the interaction of conjunction and negation. In Hungarian (Russian, Serbian, Italian, Japanese), in contrast to English (German), negated definite conjunctions are naturally and exclusively interpreted as `neither’. It is proposed that Hungarian-type languages conjunctions simply replicate the behavior of plurals, their closest semantic relatives. More puzzling is why English-type languages present a different range of interpretations. By teasing out finer distinctions in focus on connectives, syntactic structure, and context, the (...) paper tracks down missing readings and argues that it is eventually not necessary to postulate a radical cross-linguistic semantic difference. In the course of making that argument it is observed that negated conjunctions on the `neither’ reading carry the expectation that the predicate hold of both conjuncts. The paper investigates several hypotheses concerning the source of this expectation. (shrink)

Using conjunction as an example, I show a technical and philosophical problem when trying to conciliate the currently prevailing views on the meaning of logical connectives: the inferientialist (also called 'syntactic') one based on introduction and elimination rules, and the representationalist (also called 'semantic') one given through truth tables. Mostly I show that the widespread strategy of using the truth theoretical definition of logical consequence to collapse both definitions must be rejected by inferentialists. An important consequence of my argument is (...) that there are different notions of conjunction at play in standard first order logic, and that the technical and philosophical connections between them are far from well established. (shrink)

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. (shrink)

Various syntacticians have argued that coordinate structures involve a three-dimensional syntactic structure. This paper proposes an interpretation of three-dimensional syntactic structures in terms of plural reference and argues that such structures give further support for plural reference, the view that plural terms refer to several entities at once, rather than referring to a single plural individual.

Observe that complement questions can be either directly or indirectly conjoined, but they can only be indirectly disjoined. • What theories of questions and coordination predict this difference? • Look at Partition theory (Groenendijk & Stokhof 1984) and Inquisitive Semantics (Groenendijk & Roelofsen 2009, Ciardelli et al. 2012).

In many languages, the same particles that form quantifier words also serve as connectives, additive and scalar particles, question markers, roots of existential verbs, and so on. Do these have a unified semantics, or do they merely bear a family resemblance? Are they aided by silent operators in their varied roles―if yes, what operators? I dub the particles “quantifier particles” and refer to them generically with capitalized versions of the Japanese morphemes. I argue that both MO and KA can be (...) assigned a stable semantics across their various roles. The specific analysis I offer is motivated by the fact that MO and KA often combine with just one argument; I propose that this is their characteristic behavior. Their role is to impose semantic requirements that are satisfied when the immediately larger context is interpreted as the meet/join of their host’s semantic contribution with something else. They do not perform meet/join themselves. The obligatory vs. optional appearance of the particles depends on whether the meet/join interpretations arise by default in the given constellation. I explicate the proposal using the toolkit of basic Inquisitive Semantics. (shrink)