The quantified relevant logic RQ is given a new semantics in which a formula for all xA is true when there is some true proposition that implies all x-instantiations of A. Formulae are modelled as functions from variable-assignments to propositions, where a proposition is a set of worlds in a relevant model structure. A completeness proof is given for a basic quantificational system QR from which RQ is obtained by adding the axiom EC of 'extensional confinement': for all x(A (...) V B) -> (A V for all xB). with x not free in A. Validity of EC requires an additional model condition involving the boolean difference of propositions. A QR-model falsifying EC is constructed by forming the disjoint union of two natural arithmetical structures in which negation is interpreted by the minus operation. (shrink)

The exclusive component of unembedded disjunctions is standardly derived as a conversational implicature by assuming that or forms a lexical scale with and. It is well known, however, that this assumption does not suffice to determine the required scalar competitors of disjunctions with more than two atomic disjuncts (McCawley, Everything that linguists have always wanted to know about logic* (But were ashamed to ask). Chicago University Press, Chicago, 1993, p. 324; Simons, “Or”: Issues in the semantics and pragmatics of (...) disjunction. Ph.D. thesis, Cornell University, Ithaca, NY, 1998). To solve this, Sauerland (Linguist Philos 27(3): 367–391, 2004) assumes that or forms a lexical scale with two otherwise unattested silent connectives ( ${\mathbb{L}}$ and ${\mathbb{R}}$ ) that retrieve the left and right terms of a disjunction. A number of recent works have proposed an Alternative Semantics for indefinites and disjunction to account for their interaction with modals and other propositional operators (Kratzer and Shimoyama, In: Otsu Y (ed) The Proceedings of the Third Tokyo Conference on Psycholinguistics. Hituzi Syobo, Tokyo, pp. 1–25, 2002; Aloni, In: Weisgerber M (ed) Proceedings of the Conference “SuB7—Sinn und Bedeutung”. Arbeitspapier Nr. 114. Konstanz, pp. 28–37, 2003; Simons, Nat Lang Semantics 13: 271–316, 2005; Alonso-Ovalle, Disjunction in alternative semantics. Ph.D. thesis, University of Massachusetts, Amherst, MA, 2006). We note that the McCawley–Simons problem does not arise in an Alternative Semantics, if we assume that the set of pragmatic competitors to a disjunction is the closure under intersection of the set of propositions that it denotes. An adaptation of the strengthening mechanism presented in Fox (In: Sauerland U, Stateva P (eds) Presupposition and implicature in compositional semantics. MacMillan, Palgrave, pp. 71–120, 2007) allows for the derivation of the exclusive component of disjunctions with more than two atomic disjuncts without having to rely on the ${\mathbb{L}}$ and ${\mathbb{R}}$ operators. The proposal extends to the case of disjunctions with logically dependent disjuncts. (shrink)

A system FDQ of first degree entailment with quantification, extending classical quantification logic Q by an entailment connective, is axiomatised, and the choice of axioms defended and also, from another viewpoint, criticised. The system proves to be the equivalent to the first degree part of the quantified entailmental system EQ studied by Anderson and Belnap; accordingly the semantics furnished are alternative to those provided for the first degree of EQ by Belnap. A worlds semantics for FDQ is (...) presented, and the soundness and completeness of FDQ proved, the main work of the paper going into the proof of completeness. The adequacy result is applied to yield, as well as the usual corollaries, weak relevance of FDQ and the fact that FDQ is the common first degree of a wide variety of (constant domain) quantified relevant logics. Finally much unfinished business at the first degree is discussed. (shrink)

The semantical framework is fundamentally intensional: neither possible worlds nor sets as basic entities, but rather, besides individuals, propositions, properties and relations (in intension). Logical truth is defined in terms of logical form (without mentioning this notion) without employing sets of models and the concept of truth in a model. Truth itself is explicitly defined (without recursion); the truth-conditions for the logical constants of the object-language become theorems derivable from the axioms for "to intend"--the basic semantical relation.

We provide a fine-grained analysis of notions of regret and responsibility (such as agent-regret and individual responsibility) in terms of a language of multimodal logic. This language undergoes a detailed semantic analysis via two sorts of models: (i) relating models, which are equipped with a relation of propositional pertinence, and (ii) synonymy models, which are equipped with a relation of propositional synonymy. We specify a class of strictly relating models and show that each synonymy model can be transformed into an (...) equivalent strictly relating model. Moreover, we define an axiomatic system that captures the notion of validity in the class of all strictly relating models. (shrink)

This paper offers an analysis of metalinguistic comparatives such as more dumb than crazy in which they differ from ordinary comparatives in the scale on which they compare: ordinary comparatives use scales lexically determined by particular adjectives, but metalinguistic ones use a generally-available scale of imprecision or ‘pragmatic slack’. To implement this idea, I propose a novel compositional implementation of the Lasersohnian pragmatic-halos account of imprecision—one that represents clusters of similar meanings as Hamblin alternatives. In the theory that results, existential (...) closure over alternatives mediates between alternative-sets and meanings in which imprecision has been resolved. I then articulate a version of this theory in which the alternatives are not related meanings but rather related utterances, departing significantly from Lasersohn’s original conception. Although such a theory of imprecision is more clearly ‘metalinguistic’, the evidence for it from metalinguistic comparatives in English is surprisingly limited. The overall picture that emerges is one in which the grammatical distinction between ordinary and metalinguistic comparatives tracks the independently motivated distinction between vagueness and imprecision. (shrink)

This dissertation develops a substitutional semantics for first-order (modal) logic which, unlike truth-value semantics, allows a fine-grained analysis of the semantical behaviour of the terms and predicates from which atomic formulae are composed. Moreover, it proposes a nondenotational philosophical foundation for the semantics of substitutional quantified (modal) logic.

`Realism', `conceptualism' and `nominalism' are terms that one is most likely to come across in history of philosophy textbooks, presented as ones labeling three major ontological alternatives provided by mediaeval philosophy. The general inadequacy of these labels is perhaps best shown by the desperate efforts to provide further, modified labels , the well-known `moderate' and `extreme' or `exaggerated' versions of the above, in hopes of implying at least a lesser amount of falsehood in hanging..

We investigate the philosophical significance of the existence of different semantic systems with respect to which a given deductive system is sound and complete. Our case study will be Corcoran's deductive system D for Aristotelian syllogistic and some of the different semantic systems for syllogistic that have been proposed in the literature. We shall prove that they are not equivalent, in spite of D being sound and complete with respect to each of them. Beyond the specific case of syllogistic, the (...) goal is to offer a general discussion of the relations between informal notions—in this case, an informal notion of deductive validity—and logical apparatuses such as deductive systems and (model-theoretic or other) semantic systems that aim at offering technical, formal accounts of informal notions. Specifically, we will be interested in Kreisel's famous 'squeezing argument'; we shall ask ourselves what a plurality of semantic systems (understood as classes of mathematical structures) may entail for the cogency of specific applications of the squeezing argument. More generally, the analysis brings to the fore the need for criteria of adequacy for semantic systems based on mathematical structures. Without such criteria, the idea that the gap between informal and technical accounts of validity can be bridged is put under pressure. (shrink)

This paper argues that NPs with case as head noun stand for situations in their role as truthmakers within a sentential or epistemic case space. The paper develops a unified semantic analysis of case-constructions of the various sorts within a truthmaker-based version of alternative semantics.

Broad focus (or informational integration or nonautonomy) is lexically and contextually constrained, but these constraints are not well understood. On a standard theory of focus interpretation, the presupposition of a broad focus is verified whenever those of two narrow foci are. I argue that to account for cases where two narrow foci are preferred, it is necessary to assume that broad focus competes with two narrow foci and implicates the opposite of what they presuppose. Central constraints on thetic statements are (...) thus accounted for in an Optimality Theory (OT) enriched Alternative Semantics. (shrink)

Informational semantics were first developed as an interpretation of the model-theory of substructural (and especially relevant) logics. In this paper we argue that such a semantics is of independent value and that it should be considered as a genuine alternative explication of the notion of logical consequence alongside the traditional model-theoretical and the proof-theoretical accounts. Our starting point is the content-nonexpansion platitude which stipulates that an argument is valid iff the content of the conclusion does not exceed (...) the combined content of the premises. We show that this basic platitude can be used to characterise the extension of classical as well as non-classical consequence relations. The distinctive trait of an informational semantics is that truth-conditions are replaced by information-conditions. The latter leads to an inversion of the usual order of explanation: Considerations about logical discrimination (how finely propositions are individuated) are conceptually prior to considerations about deductive strength. Because this allows us to bypass considerations about truth, an informational semantics provides an attractive and metaphysically unencumbered account of logical consequence, non-classical logics, logical rivalry and pluralism about logical consequence. (shrink)

This paper presents a systematic semantic study of constructions with the noun 'case'. It argues that 'cases' are situations acting as truthmakers within a sentential or epistemic case space. It develops a truthmaker-based alternative semantics of 'case'-constructions, based on Fine's recent truthmaker semantics.

Conversational negation often behaves differently from negation as a logical operator: when rejecting a state of affairs, it does not present all members of the complement set as equally plausible alternatives, but it rather suggests some of them as more plausible than others (e.g., “This is not a dog, it is a wolf/*screwdriver”). Entities that are semantically similar to a negated entity tend to be judged as better alternatives (Kruszewski et al., 2016). In fact, Kruszewski et al. (2016) show that (...) the cosine similarity scores between the distributional semantics representations of a negated noun and its potential alternatives are highly correlated with the negated noun-alternatives human plausibility ratings. In a series of cloze tasks, we show that negation likewise restricts the production of plausible alternatives to similar entities. Furthermore, completions to negative sentences appear to be even more restricted than completions to an affirmative conjunctive context, hinting at a peculiarity of negation. (shrink)

Natural language conditionals seem to be subject to three logical requirements: they invalidate Antecedent Strengthening, they validate so-called Simplification of Disjunctive Antecedents, and they allow for the replacement of logically equivalent clauses in antecedent position. Unfortunately, these requirements are jointly inconsistent. Conservative solutions to the puzzle drop Simplification, treating it as a pragmatic inference. I show that pragmatic accounts of Simplification fail, and develop a truthmaker semantics for conditionals that captures all the relevant data. Differently from existing truthmaker (...) class='Hi'>semantics, my semantics extends, rather than replaces, standard possible worlds semantics. The main innovation is the notion of a truthmaker in play: this notion is cognitive, rather than metaphysical, and can be defined in a purely syntactic way. (shrink)

Alternatives in Semantics is the first volume to focus on alternatives as a key theme. It offers a survey of the use of alternatives in semantics and pragmatics, and an overview of current approaches and applications of alternative-based semantics, from both theoretical and experimental perspectives. The chapters represent different theoretical frameworks, which differ in the way they conceive of the source of alternatives, the status of alternatives, or the precise way in which they enter semantic composition. (...) The contributions focus on various empirical phenomena making reference to alternatives (negative polarity and free choice phenomena, implicatures, presupposition, focus and intervention effects), offering new insights and exploring connections between them. The chapters assembled in this volume demonstrate the vitality of alternative-based semantics and offer a clear perspective on the many challenging questions that arise from its increasing range of applications. (shrink)

Cerrito has proposed a declarative semantics for allowed logic programs using Girard's linear logic, with weakening. We propose an alternative semantics using pure linear logic. The main difference between our approach and that of Cerrito is that the comma of a logic program is interpreted as the multiplicative connective instead of the additive &. This enables us to establish a soundness result without the introduction of the projection symbols employed by Cerrito. The price to be paid for (...) this simplification occurs in the establishment of a completeness result. Our definition of the completed program is more complicated than that given by Cerrito. We establish a completeness result for the class of allowed programs and queries using our definition of the program completion. (shrink)

Aspectual particles (the term is due to (König 1991)) appear to come in groups, related by negation, and therefore have attracted the attention of formal semanticists. The following examples list the particles of English, German and Hebrew; they show that the system is semantically transparent in various degrees.

Existence monism (EM) is a metaphysical view asserting the existence of only one concrete object. EM is well known for its radicalness, and encounters difficulty in terms of its prima facie inconsistency with truisms. This paper aims to propose an alternative (and somewhat easy) way to overcome this difficulty and indicate another means by which the possibility of EM can be defended. I will present a package of theses that are intended to be combined with EM, which I call (...) Linguistic Ontology with the One as Semantic Glue (LOOSG). I will show that this package (in combination with EM) provides a systematic explanation as to why truisms hold while only one concrete object actually exists. In other words, I will argue that if an existence monist embraces LOOSG, the desired explanation for truisms is then available to her. In addition, it will also be noted that LOOSG has a theoretical virtue, in that it only presupposes the framework of standard semantics. Based on these discussions, I offer LOOSG as a viable option for existence monism. (shrink)

Fish abound in the pond Garlic reeked on his breath The pond abounds with fish His breath reeked with garlic Such sentences were first noted in Jespersen, then were introduced in Generative Grammar by Fillmore and Anderson. The most extensive treatment, from which some of the data below is taken, is Salkoff’s ”Bees are Swarming in the Garden”, Language 59.2, 288-346; cf. also Boons & Leclere, and see Levin for further references. For convenience in referring to the two kinds of (...) sentences, I will adopt this terminology: Agent-Subject Form: “Bees are swarming in the garden” Location-Subject Form: “The garden is swarming with bees” The swarm-alternation should be distinguished carefully from the spray-load -alternation. (shrink)

Russell and Strawson sparked a well known debate on the subject of Linguistic Presupposition inspiring many linguists and philosophers to follow suit, including Frege, whose work initiated the modern study in this area. Beaver begins with the most comprehensive overview and critical discussion of this burgeoning field published to date. He then goes on to motivate and develop his own account based on a Dynamic Semantics. This account is a recent line of theoretical work in which the Tarskian emphasis (...) on truth conditions is questioned. The central plank of the theory of meaning is a formal account of the change in information effected by use of language on hearers or readers. The proposal thus consolidates ideas of Stalnaker, Karttunen and Heim, all of whom had suggested that such an account was needed. At the same time it provides a new impulse and motivation to Dynamic Semantics itself. (shrink)

One of the difficult areas for persons learning a foreign language is to grasp the range of usages of syntactic patterns that exist in the foreign language. It is not sufficient to learn how passive formation works, or how pre- or postpositional phrases are constructed, or how perfect tenses are expressed. One also has to learn which verbs can passivize at all, which verbs go with which pre- or postpositions, and, in case perfect tenses are expressed, as in a number (...) of European languages, with different auxiliaries like ‘have’ and ‘be’, which verb needs which auxiliary. For English, Levin (1993) distinguishes no less than 57 verb classes, most of them with a number of subclasses, that show distinct syntactic behavior. (shrink)

Social representations research has tended to focus upon the representations that groups have in relation to some object. The present article elaborates the concept of social representations by pointing to the existence of “alternative representations” as sub-components within social representations. Alternative representations are the ideas and images the group has about how other groups represent the given object. Alternative representations are thus representations of other people's representations. The present article uses data from Moscovici's analysis of the diffusion (...) of psychoanalysis to examine how people engage with alternative representations. It is demonstrated that there can be more or less dialogical relations with alternative representations. The analysis concludes by considering seven “semiotic barriers” which work to neutralise the dialogical potential of alternative representations, thus on the one hand enabling groups to talk about the views of others, while, on the other hand, remaining unchallenged by those views. (shrink)

American-plan semantics with 4 values 1, 0, { {1, 0}} {{}}, interpretable as True, False, Both and Neither, are furnished for a range of logics, including relevant affixing systems. The evaluation rules for extensional connectives take a classical form: in particular, those for negation assume the form 1 (A, a) iff 0 (A, a) and 0 (A, a) iff 1 (A, a), so eliminating the star function *, on which much criticism of relevant logic semantics has focussed. The (...) cost of these classical features is a further relation (or operation), required in evaluating falsity assignments of implication formulae.Two styles of 4 valued relational semantics are developed; firstly a semantics using notions of double truth and double validity for basic relevant systemB and some extensions of it; and secondly, since the first semantics makes heavy weather of validating negation principles such as Contraposition, a reduced semantics using more complex implicational rules for relevant systemC and various of its extensions. To deal satisfactorily with elite systemsR,E andT, however, further complication is inevitable; and a relation of mateship (suggested by the Australian plan) is introduced to permit cross-over from 1 to 0 values and vice versa. (shrink)

In virtue of what do the utterances we make mean what they do? What facts about these signs, about us, and about our environment make it the case that they have the meanings they do? According to a tradition stemming from H.P. Grice through David Lewis and Stephen Schiffer it is in virtue of facts about conventions that we participate in as language users that our utterances mean what they do (see Gr'ice 1957, Lewis 1969, 1983, Schiffer 1972, 1982). This (...) view currently enjoys widespread acceptance among philosophers of mind and language. Though most are not particularly interested in the details of such programs, the dominant view seems to be that something of the sort proposed by Grice, Lewis and Schiffer is basically right. Thus, Jerry Fodor, refiecting what I take to be prevalent attitudes in the field, writes. (shrink)

In virtue of what do the utterances we make mean what they do? What facts about these signs, about us, and about our environment make it the case that they have the meanings they do? According to a tradition stemming from H.P. Grice through David Lewis and Stephen Schiffer it is in virtue of facts about conventions that we participate in as language users that our utterances mean what they do (see Gr'ice 1957, Lewis 1969, 1983, Schiffer 1972, 1982). This (...) view currently enjoys widespread acceptance among philosophers of mind and language. Though most are not particularly interested in the details of such programs, the dominant view seems to be that something of the sort proposed by Grice, Lewis and Schiffer is basically right. Thus, Jerry Fodor, refiecting what I take to be prevalent attitudes in the field, writes. (shrink)

The semantics for a deontic action logic based on Boolean algebra is extended with an interpretation of action expressions in terms of sets of alternative actions, intended as a way to model choice. This results in a non-classical interpretation of action expressions, while sentences not in the scope of deontic operators are kept classical. A deontic structure based on Simons’ supercover semantics is used to interpret permission and obligation. It is argued that these constructions provide ways to (...) handle various problems related to free choice permission. The main result is a sound and complete axiomatization of the semantics. (shrink)

In classical logic, the proposition expressed by a sentence is construed as a set of possible worlds, capturing the informative content of the sentence. However, sentences in natural language are not only used to provide information, but also to request information. Thus, natural language semantics requires a logical framework whose notion of meaning does not only embody informative content, but also inquisitive content. This paper develops the algebraic foundations for such a framework. We argue that propositions, in order to (...) embody both informative and inquisitive content in a satisfactory way, should be defined as non-empty, downward closed sets of possibilities, where each possibility in turn is a set of possible worlds. We define a natural entailment order over such propositions, capturing when one proposition is at least as informative and inquisitive as another, and we show that this entailment order gives rise to a complete Heyting algebra, with meet, join, and relative pseudo-complement operators. Just as in classical logic, these semantic operators are then associated with the logical constants in a first-order language. We explore the logical properties of the resulting system and discuss its significance for natural language semantics. We show that the system essentially coincides with the simplest and most well-understood existing implementation of inquisitive semantics, and that its treatment of disjunction and existentials also concurs with recent work in alternative semantics. Thus, our algebraic considerations do not lead to a wholly new treatment of the logical constants, but rather provide more solid foundations for some of the existing proposals. (shrink)

Most theories of semantic competence in natural language implicitly assume the Language of Thought Hypothesis. According to this hypothesis, all human cognition consists in the deployment of a language of thought. This language of thought is supposed to be independent of natural language, yet at the same time, it is supposed to be semantically isomorphic with natural language. Given this assumption, it is easy to answer basic questions regarding semantic competence in natural language. What are semantic properties of natural language, (...) and how did they originate? Natural language inherits the semantic properties of the language of thought it is used to express. What does semantic competence consist in? It consists in knowing how to translate items in one's language of thought into a public medium. ;The starting point of this dissertation is the rejection, by some prominent paradigms in cognitive science, of the view that human cognition consists in the deployment of a language of thought that is, at the same time, independent of natural language, yet semantically isomorphic with it. The dissertation constitutes a fledgling attempt to explore an alternative approach to explaining semantic competence in natural language, an approach that is compatible with this rejection of the Language of Thought Hypothesis. ;Rather than conceive of natural language as a tool for expressing items in a pre-existing, semantically isomorphic, language of thought, I urge that language be conceived of as a norm-governed social practice. On this view, the semantic properties of natural language are determined by the inferential norms governing linguistic performances. In order to explain the origin of its semantic properties, one must explain the origin of the inferential norms that govern language. In order to explain what semantic competence consists in, one must explain how individuals learn to abide by these inferential norms. The bulk of the dissertation is devoted to showing that neither of these explanatory projects requires endorsing the Language of Thought Hypothesis. I do this by sketching the form that such explanations might take, and showing that they are consistent with much current research in ethology, comparative psychology, developmental psychology, and evolutionary biology. (shrink)

Over a longer period than I sometimes care to contemplate I have worked on possible-worlds semantics. The earliest work was in modal logic, to which I keep returning, but a sabbatical in 1970 took me to UCLA, there to discover the work of Richard Montague in applying possible-worlds semantics to natural lan guage. My own version of this appeared in Cresswell (1973) and was followed up in a number of articles, most of which were collected in Cresswell (1985b). (...) A central problem for possible worlds semantics is how to accommodate propositional attitudes. This problem was addressed in Cresswell (1985a), and the three books mentioned so far represent a reasonably complete picture of my positive views on formal semantics. I have regarded the presentation of a positive view as more important than the criticism of alternatives, although the works referred to do contain many passages in which I have tried to defend my own views against those of others. But such criticism is important in that a crucial element in establishing the content of a theory is that we be able to evaluate it in relation to its com petitors. It is for that reason that I have collected in this volume a number of articles in which I attempt to defend the positive semantical picture I favour against objections and competing theories. (shrink)