In this article we tackle the issue of diachronic variation in constructional semantics through an exploration of the (recent) semantic history of the well-established English ditransitive or double object argument structure construction. Starting from the assumption that schematic syntactic patterns are not fundamentally different from lexical items, we will show that — similar to the diachronic semantic development of lexemes — the semantics of argument structure constructions in general and that of double object constructions in particular, is (...) vulnerable to semasiological shifts as well. More specifically, the analysis, which compares data from 18th-century Late Modern English with present-day English, shows that the double object construction's semantic evolution presents a case of specialization, in which the construction has come to be associated with a significantly narrower range of meanings. It will further be argued that such patterns of semantic change are best captured in a model of argument structure semantics which discriminates between central and lesscentral or prototypical and non-prototypical uses. (shrink)

This paper provides a constructive topological semantics for non-deducibility of a first order intuitionistic formula. Formal topology theory, in particular the recently introduced notion of a binary positivity predicate, and co-induction are two needful tools.

In 1933 Godel introduced a calculus of provability (also known as modal logic S4) and left open the question of its exact intended semantics. In this paper we give a solution to this problem. We find the logic LP of propositions and proofs and show that Godel's provability calculus is nothing but the forgetful projection of LP. This also achieves Godel's objective of defining intuitionistic propositional logic Int via classical proofs and provides a Brouwer-Heyting-Kolmogorov style provability semantics for (...) Int which resisted formalization since the early 1930s. LP may be regarded as a unified underlying structure for intuitionistic, modal logics, typed combinatory logic and λ-calculus. (shrink)

Computational models of semantic memory exploit information about co-occurrences of words in naturally occurring text to extract information about the meaning of the words that are present in the language. Such models implicitly specify a representation of temporal context. Depending on the model, words are said to have occurred in the same context if they are presented within a moving window, within the same sentence, or within the same document. The temporal context model (TCM), which specifies a particular definition of (...) temporal context, has proved useful in the study of episodic memory. The predictive temporal context model (pTCM) uses the same definition of temporal context to generate semantic memory representations. Taken together pTCM and TCM may prove to be part of a general model of declarative memory. (shrink)

This edited book brings together research work in the field of constructive semantics with scholarship on the phenomenological foundations of logic and mathematics. It addresses one of the central issues in the epistemology and philosophy of mathematics, namely the relationship between phenomenological meaning constitution and constructive semantics. Contributing authors explore deep structural connections and fundamental differences between phenomenology and constructivism. Papers are drawn from contributions to a prestigious workshop held at the University of Friedrichshafen. Readers will discover insight (...) into structural connections between the phenomenological concept of meaning constitution and constructivist concepts of meaning. Discussion ranges from more specific conceptualizations in the philosophy of logic and mathematics to more general considerations in epistemology, inferential semantics and phenomenology. Questions such as a possible phenomenological understanding of the relationship between structural rules and particle rules in dialogical logic are explored. Significant aspects of both phenomenology and dialectics, and dialectics and constructivism emerge. Graduates and researchers of philosophy, especially logic, as well as scholars of mathematics will all find something of interest in the expert insights presented in this volume. (shrink)

A number of recent models of semantics combine linguistic information, derived from text corpora, and visual information, derived from image collections, demonstrating that the resulting multimodal models are better than either of their unimodal counterparts, in accounting for behavioral data. Empirical work on semantic processing has shown that emotion also plays an important role especially in abstract concepts; however, models integrating emotion along with linguistic and visual information are lacking. Here, we first improve on visual and affective representations, derived (...) from state‐of‐the‐art existing models, by choosing models that best fit available human semantic data and extending the number of concepts they cover. Crucially then, we assess whether adding affective representations (obtained from a neural network model designed to predict emojis from co‐occurring text) improves the model's ability to fit semantic similarity/relatedness judgments from a purely linguistic and linguistic–visual model. We find that, given specific weights assigned to the models, adding both visual and affective representations improves performance, with visual representations providing an improvement especially for more concrete words, and affective representations improving especially the fit for more abstract words. (shrink)

In this article we firstly present a Kripke semantics for the description logic ALC which is directly inspired by the semantics for Intuitionistic logic. Moreover, we discuss why a direct translation of this kind of semantics is not adequate in the description logic context and propose a constructive semantics that differs from the previous one by the fact that we impose a condition on the partial order. We also present a tableau calculus which is sound and (...) complete with respect to our semantics. As an application of the calculus we prove that this semantics meets the disjunction property, a key criterion used in assessing whether a logic is constructive. (shrink)

Editorial NoteThis lecture was given by Per Martin-Löf at Leiden University on August 25, 2001 at the invitation by Göran Sundholm to address the topic mentioned in the title and to reflect on Dummett’s earlier effort of almost a decade before. The lecture was part of a three-day conference on Gottlob Frege. Sundholm arranged for the lecture to be recorded and commissioned Bjørn Jespersen to make a transcript. The information in footnote 1, which Sundholm provided, has been independently confirmed by (...) Thomas Ricketts in an email to the author. The present version has been edited by Ansten Klev. Following the displayed text there is a lacuna in the original transcript corresponding to a pause in the recording when the tape was changed. The continuous text of the present version is the result of a few additions to the original transcript suggested by Klev and agreed to by the author. (shrink)

Semantic Leaps explores how people combine knowledge from different domains in order to understand and express new ideas. Concentrating on dynamic aspects of on-line meaning construction, Coulson identifies two related sets of processes: frame-shifting and conceptual blending. Frame-shifting is semantic reanalysis in which existing elements in the contextual representation are reorganized into a new frame. Conceptual blending is a set of cognitive operations for combining partial cognitive models. By addressing linguistic phenomena often ignored in traditional meaning research, Coulson explains how (...) processes of cross-domain mapping, frame-shifting, and conceptual blending enhance the explanatory adequacy of traditional frame-based systems for natural language processing. The focus is on how the constructive processes speakers use to assemble, link, and adapt simple cognitive models underlie a broad range of productive language behavior. (shrink)

1st GPMR Workshop on Logic and Semantics: Medieval Logic and Modern Applied Logic, Reinische Friedrich Wilhelms Universität Bonn, Germany, 2007.

Regarding constructivism as a learning philosophy and/or a model of knowing, a person (learner or mentor) based on her/ his preconceptions and on personal knowings could actively participate in an interaction with another person (learner or mentor) in order to construct her/his personal knowledge. In this research I will analyse 'meaning construction' within constructivism. I will focus on a semantic loop that the learner and mentor as intentional participants move through and organise their personal constructed conceptions in order to construct (...) meanings and produce their individual meaningful comprehensions. Subsequently, I will provide a semantic framework for analysing the meaning construction based on personal knowings and personal conceptions within constructivist interactions. This research could propose a new scheme for interpretation based on semantics and on interaction. (shrink)

Sheaf semantics is developed within a constructive and predicative framework, Martin‐Löf's type theory. We prove strong completeness of many sorted, first order intuitionistic logic with respect to this semantics, by using sites of provably functional relations.

A semantics for quantified modal logic is presented that is based on Kleene's notion of realizability. This semantics generalizes Flagg's 1985 construction of a model of a modal version of Church's Thesis and first-order arithmetic. While the bulk of the paper is devoted to developing the details of the semantics, to illustrate the scope of this approach, we show that the construction produces (i) a model of a modal version of Church's Thesis and a variant of a (...) modal set theory due to Goodman and Scedrov, (ii) a model of a modal version of Troelstra's generalized continuity principle together with a fragment of second-order arithmetic, and (iii) a model based on Scott's graph model (for the untyped lambda calculus) which witnesses the failure of the stability of non-identity. (shrink)

In a first part, I defend that formal semantics can be used as a guide to ontological commitment. Thus, if one endorses an ontological view \(O\) and wants to interpret a formal language \(L\) , a thorough understanding of the relation between semantics and ontology will help us to construct a semantics for \(L\) in such a way that its ontological commitment will be in perfect accordance with \(O\) . Basically, that is what I call constructing formal (...) semantics from an ontological perspective. In the rest of the paper, I develop rigorously and put into practice such a method, especially concerning the interpretation of second-order quantification. I will define the notion of ontological framework: it is a set-theoretical structure from which one can construct semantics whose ontological commitments correspond exactly to a given ontological view. I will define five ontological frameworks corresponding respectively to: (i) predicate nominalism, (ii) resemblance nominalism, (iii) armstrongian realism, (iv) platonic realism, and (v) tropism. From those different frameworks, I will construct different semantics for first-order and second-order languages. Notably I will present different kinds of nominalist semantics for second-order languages, showing thus that we can perfectly quantify over properties and relations while being ontologically committed only to individuals. I will show in what extent those semantics differ from each other; it will make clear how the disagreements between the ontological views extend from ontology to logic, and thus why endorsing an ontological view should have an impact on the kind of logic one should use. (shrink)

Questo contributo tratta della perifrasi ‘εἶναι + participio’ in greco omerico all’interfaccia fra morfosintassi e semantica. I dati sono analizzati con riferimento al quadro teorico elaborato da Nardi e Romagno (2022), che considerano la perifrasi con εἶναι in greco antico come una categoria prototipica: secondo questa prospettiva, la categoria sovraordinata ‘εἶναι + participio’ include due manifestazioni formalmente diverse ma funzionalmente equivalenti, un costrutto con una copula espressa, cioè una perifrasi vera e propria, e un costrutto senza copula espressa, cioè un (...) participio predicativo (fondamentalmente, un participio che funziona come una forma finita). Questa indagine mira a valutare se si possano individuare fattori che determinano o soggiacciono all’uso di queste costruzioni participiali in greco omerico. L’analisi dei dati raccolti nei poemi omerici mostra che le costruzioni participiali codificano la funzione specifica di significare lo stato, inerente o acquisito, del soggetto del predicato, costituendo pertanto un’alternativa (più o meno libera) al perfetto originario (cfr. Romagno 2005). (shrink)

(1) is an example of an adjectival comparative. In it, the adjective important is flanked by more and a comparative clause headed by than. This article is a survey of recent ideas about the interpretation of comparatives, including (i) the underlying semantics based on the idea of a threshold; (ii) the interpretation of comparative clauses that include quantifiers (brighter than on many other days); (iii) remarks on differentials such as much in (1) above: what they do in the comparative (...) and what they do elsewhere in the language; (iv) the relationship between comparatives and other Degree constructions (e.g. as important, too impor- tant); and (v) the types of phrases in which comparatives are found (adjective: tighter versus noun: more water). Given the nature and purpose of this essay, I have tried not to presuppose background in formal semantics and I have departed from standard practice in journal articles by, as much as possible, not interrupting the flow with footnotes and references. There are two appendices. The first provides more analytical detail and there I do rely on formal techniques of natural language semantics. The second covers the sources for the ideas surveyed here. (shrink)

A language is specified by a Lexicon and a Grammar. A constructive grammar goes like this: The Lexicon provides a set of items. The items are associated with Categories and Denotations. The Grammar gives a recursive specification of the language by defining sets of derived expressions starting with the Lexicon as the base and allowing the combination of lexical items into expressions with their Categories and Denotations, by a rule-to-rule procedure, and so on ad libitum.

In (1b), for the most part induces a so-called Quantificational Variability Effect (QVE) on the NP the linguists from the East Coast, yielding roughly the interpretation ‘most of the linguists from the East Coast came to NELS’. We claim that the two constructions above differ in the domain where they apply, producing similar but not identical quantificational interpretations over the NP. In particular, we argue that most of the NPs applies to the nominal domain, while for the most part applies (...) to the verbal domain. Our claim is based on two sets of novel semantic data. First, we show that the distribution of most of the NPs is parallel to that of all the NPs in terms of its selective compatibility with collective predicates. To account for this data, we extend Brisson’s (1998, 2003) analysis of all the NPs to most of the NPs, concluding that most is an ∃-quantifier introducing a group of a certain proportion. Second, we show that, when for the most part gives rise to a QVE on a definite NP, the collective interpretation is not available. We develop a semantic analysis of for the most part as a verbal modifier that explains the lack of collective readings and that extends to interpretations other than QVE. The structure of the paper is as follows: in section 2, we introduce some general background on events and distributivity that are relevant to the current paper. In section 3, we propose the analysis of most of the NPs, followed by the analysis of for the most part in section 4. Section 5 concludes the paper and discusses further issues. (shrink)

We introduce a general notion of semantic structure for first-order theories, covering a variety of constructions such as Tarski and Kripke semantics, and prove that, over Zermelo–Fraenkel set theory, the completeness of such semantics is equivalent to the Boolean prime ideal theorem. Using a result of McCarty, we conclude that the completeness of Kripke semantics is equivalent, over intuitionistic Zermelo–Fraenkel set theory, to the Law of Excluded Middle plus BPI. Along the way, we also prove the equivalence, (...) over ZF, between BPI and the completeness theorem for Kripke semantics for both first-order and propositional theories. (shrink)

This paper investigates whether an abstract linguistic construction shows the kind of prototype effects characteristic of non-linguistic categories, in both adults and young children. Adapting the prototype-plus-distortion methodology of Franks and Bransford (1971), we found that whereas adults were lured toward false-positive recognition of sentences with prototypical transitive semantics, young children showed no such effect. We examined two main implications of the results. First, it adds a novel data point to a growing body of research in cognitive linguistics and (...) construction grammar that shows abstract linguistic categories can behave in similar ways to non-linguistic categories, for example, by showing graded membership of a category. Thus, the findings lend psychological validity to the existing cross-linguistic evidence for prototypical transitive semantics. Second, we discuss a possible explanation for the fact that prototypical sentences were processed differently in adults and children, namely, that children’s transitive semantic network is not as interconnected or cognitively coherent as adults’. (shrink)

Among Dunn’s many important contributions to relevance logic was his work on the system RM (R-mingle). Although RM is an interesting system in its own right, it is widely considered to be too strong. In this chapter, I revisit a closely related system, RM0 (sometimes known as ‘constructive mingle’), which includes the mingle axiom while not degenerating in the way that RM itself does. My main interest will be in examining this logic from two related semantical perspectives. First, I give (...) a purely operational bisemilattice semantics for it by adapting previous work of Humberstone. Second, I examine a more conventional algebraic semantics for it and discuss how this relates to the operational semantics. A novel operational semantics for J (intuitionistic logic) as well as its conventional Heyting algebraic semantics emerge as special cases of the corresponding semantics for RM0. The results of this chapter suggest that RM0 is a more interesting logic than has been appreciated and that Humberstone’s operational semantic framework similarly deserves more attention than it has received. (shrink)

I present a semantics for the language of first-order additive-multiplicative linear logic, i.e. the language of classical first-order logic with two sorts of disjunction and conjunction. The semantics allows us to capture intuitions often associated with linear logic or constructivism such as sentences = games, SENTENCES = resources or sentences = problems, where “truth” means existence of an effective winning strategy.The paper introduces a decidable first-order logic ET in the above language and gives a proof of its soundness (...) and completeness with respect to this semantics. Allowing noneffective strategies in the latter is shown to lead to classical logic.The semantics presented here is very similar to Blass's game semantics. Although there is no straightforward reduction between the two corresponding notions of validity, my completeness proof can likely be adapted to the logic induced by Blass's semantics to show its decidability, which was the main problem left open in Blass's paper.The reader needs to be familiar with classical logic and arithmetic. (shrink)

Split constructions are widespread in natural languages. The separation of the semantic restriction of a quantifier from that quantifier is a typical example of such a construction. This study addresses the problem that such discontinuous strings exhibit--namely, a number of locality constraints, including intervention effects. These are shown to follow from the interaction of a minimalist syntax with a semantics that directly assigns a model-theoretic interpretation to syntactic logical forms. The approach is shown to have wide empirical coverage and (...) a conceptual simplicity. The book will be of interest to scholars and advanced students of syntax and semantics. (shrink)

A central tenet of cognitive linguistics is that adults’ knowledge of language consists of a structured inventory of constructions, including various two-argument constructions such as the active, the passive and “fronting” constructions. But how do speakers choose which construction to use for a particular utterance, given constraints such as discourse/information structure and the semantic fit between verb and construction? The goal of the present study was to build a computational model of this phenomenon for two-argument constructions in Mandarin. First, we (...) conducted a grammaticality judgment study with 60 native speakers which demonstrated that, across 57 verbs, semantic affectedness – as determined by further 16 native speakers – predicted each verb’s relative acceptability in the bei-passive and ba-active constructions, but not the Notional Passive and SVO Active constructions. Second, in order to simulate acquisition of these competing constraints, we built a computational model that learns to map from corpus-derived input to an output representation corresponding to these four constructions. The model was able to predict judgments of the relative acceptability of the test verbs in the ba-active and bei-passive constructions obtained in Study 1, with model-human correlations in the region of r = 0.5 and r = 0.3, respectively. Surprisingly, these correlations increased when lexical verb identity was removed; perhaps because this information leads to over-fitting of the training set. These findings suggest the intriguing possibility that acquiring constructions involves forgetting as a mechanism for abstracting across certain fine-grained lexical details and idiosyncrasies. (shrink)

Montague’s framework for semantic interpretation has always been less well adapted to the interpretation of words than of syntactic constructions. In the late 1970s, David Dowty addressed this problem, concentrating on the interpretation of tense, aspect, inchoatives, and causatives in an extension of Montague’s Intensional Logic. In this paper I will try to revive this project, conceiving it as part of a larger task aiming at the interpretation of derivational morphology. I will try to identity some obstacles arising in Dowty’s (...) approach, and will suggest an alternative approach that, while it does not provide a global interpretation of causality, seems to work well with a wide range of the causal constructions that are important in word formation. I try to relate these ideas to some themes in contemporary philosophy and in the formalization of commonsense reasoning. (shrink)

First published in 1997, this book addresses the question: What is the interpretation of English there-existential construction? One of the principal goals is to develop an interpretation for the construction that will specifically address other properties of the postcopular DP. After outlining the problem, the author goes on to present a syntactic motivation for the claim that the postcopular DP is the sole complement to the existential predicate, as well as for the claim that the optional final phrase is a (...) predictive adjunct. In chapter 3 the interpretation for the basic existential construction is developed and then compared to analyses that take the postcopular DP to denote an ordinary individual or a generalised quantifier of individuals. This analysis is then augmented to account for the contribution of the final XP and shows how the predicate restriction can be derived from a more general condition on depictive/circumstantial VP-adjuncts. The final chapter contain some speculative discussion of the broader implications of the proposal in the context of data such as "list" existential and "presentational-there" sentences. (shrink)

This paper presents a constructive interpretation for the proofs in classical logic of $\Sigma^0_1$ -sentences and for a witness extraction procedure based on Prawitz's reduction rules.

: This study describes a new field method, suited for investigating scope relations — and other aspects of truth conditional meaning — with native speaker consultants who may speak no other language and have no background in linguistics or logic. This method revealed a surprising scope contrast between the antipassive and the ergative construction in Greenlandic Eskimo. The results of this field work are described in detail and a crosslinguistic scope generalization is proposed based on Greenlandic Eskimo, Basque, Polish, Russian, (...) Finnish and English. (shrink)

Measuring event-related potentials (ERPs) has been fundamental to our understanding of how language is encoded in the brain. One particular ERP response, the N400 response, has been especially influential as an index of lexical and semantic processing. However, there remains a lack of consensus on the interpretation of this component. Resolving this issue has important consequences for neural models of language comprehension. Here we show that evidence bearing on where the N400 response is generated provides key insights into what it (...) reflects. A neuroanatomical model of semantic processing is used as a guide to interpret the pattern of activated regions in functional MRI, magnetoencephalography and intracranial recordings that are associated with contextual semantic manipulations that lead to N400 effects. (shrink)