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Published: 11 March 2023

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1

van, Deemter Kees, and Peters Stanley 1941-, eds. Semantic ambiguity and underspecification. Stanford, Calif: CSLI Publications, 1996.

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2

Morrill, Glyn V. Categorial grammar: Logical syntax, semantics, and processing. Oxford: Oxford University Press, 2011.

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3

Steksova, T. I. Semantika nevolʹnosti v russkom i͡a︡zyke: Znachenie, vyrazhenie, funkt͡s︡ii. Novosibirsk: Novosibirskiĭ gos. pedagog. universitet, 2002.

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4

The elements of mathematical semantics. Berlin: Mouton de Gruyter, 1992.

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5

Morrill, Glyn V. Type logical grammar: Categorial logic of signs. Dordrecht: Springer Science, 1994.

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6

Morrill, Glyn V. Type logical grammar: Categorial logic of signs. Dordrecht: Kluwer Academic Publishers, 1994.

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7

Hasegawa, Masahito. Models of Sharing Graphs: A Categorical Semantics of let and letrec. London: Springer London, 1999.

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8

Hasegawa, Masahito. Models of sharing graphs: A categorical semantics of let and letrec. New York: Springer, 1999.

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9

Moortgat, Michael. Categorial investigations: Logical and linguistic aspects of the Lambek calculus. Dordrecht, Holland: Foris Publications, 1988.

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10

Events, arguments, and aspects: Topics in the semantics of verbs. Amsterdam: John Benjamins Publishing Company, 2014.

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11

Yuasa, Etsuyo. Modularity in language: Constructional and categorial mismatch in syntax and semantics. Berlin: Mouton de Gruyter, 2005.

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12

Christian, Retoré, and SpringerLink (Online service), eds. The Logic of Categorial Grammars: A Deductive Account of Natural Language Syntax and Semantics. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012.

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13

Aspects of a theory of singular reference: Prolegomena to a dialectical logic of singular terms. New York: Garland Pub., 1985.

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14

1953-, Szabolcsi Anna, ed. Ways of scope taking. Dordrecht: Kluwer Academic Publishers, 1997.

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15

Casadio, C. Significato e categorie. Bologna: CLUEB, 1987.

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16

Copulas: Universals in the categorization of the lexicon. Oxford: Oxford University Press, 2003.

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17

Casadio, C. Logic for grammar: Developments in linear logic and formal linguistics. Roma: Bulzoni, 2002.

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18

Makkai, Mihály. Models, logics, and higher-dimensional categories: A tribute to the work of Mihaly Makkai. Providence, R.I: American Mathematical Society, 2011.

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19

Kishida, Kohei. Categories and Modalities. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198748991.003.0009.

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Category theory provides various guiding principles for modal logic and its semantic modeling. In particular, Stone duality, or “syntax-semantics duality”, has been a prominent theme in semantics of modal logic since the early days of modern modal logic. This chapter focuses on duality and a few other categorical principles, and brings to light how they underlie a variety of concepts, constructions, and facts in philosophical applications as well as the model theory of modal logic. In the first half of the chapter, I review the syntax-semantics duality and illustrate some of its functions in Kripke semantics and topological semantics for propositional modal logic. In the second half, taking Kripke’s semantics for quantified modal logic and David Lewis’s counterpart theory as examples, I demonstrate how we can dissect and analyze assumptions behind different semantics for first-order modal logic from a structural and unifying perspective of category theory. (As an example, I give an analysis of the import of the converse Barcan formula that goes farther than just “increasing domains”.) It will be made clear that categorical principles play essential roles behind the interaction between logic, semantics, and ontology, and that category theory provides powerful methods that help us both mathematically and philosophically in the investigation of modal logic.
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20

Morrill, Glyn. Categorial Grammar : Logical Syntax, Semantics, and Processing: Logical Syntax, Semantics, and Processing. Oxford University Press, 2011.

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21

Mithun, Marianne. Argument Marking in the Polysynthetic Verb and Its Implications. Edited by Michael Fortescue, Marianne Mithun, and Nicholas Evans. Oxford University Press, 2017. http://dx.doi.org/10.1093/oxfordhb/9780199683208.013.4.

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It is generally agreed that the essence of polysynthesis goes beyond sheer numbers of morphemes per word, but which other properties might be criterial is unclear. Most frequently cited is the marking of core arguments within the verb, such that the key elements of the clause, predicate, and arguments, are contained within that one word. Also often cited are noun incorporation, applicatives, rich inventories of adverbial affixes, and pragmatically motivated word order. But argument marking on the verb is not categorical: pronominal affix paradigms show a range of differential marking patterns dependent on various semantic and grammatical features, none reliably predictive of other characteristics typically associated with polysynthesis. Yet these characteristics tend to cluster, indicating that they are not reflections of a single, underlying governing principle, but rather constitute structural complexes that emerge from constellations of cognitive and social factors favoring the development and maintenance of complex morphologies.
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22

Bell, John L. Categorical Logic and Model Theory. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198748991.003.0007.

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The chapter begins with an introduction describing the development of categorical logic from the 1960s. The next section, `Categories and Deductive Systems’, describes the relationship between categories and propositional logic, while the ensuing section, `Functorial Semantics’, is devoted to Lawvere’s provision of the first-order theory of models with a categorical formulation. In the section `Local Set Theories and Toposes’ the categorical counterparts—toposes—to higher-order logic are introduced, along with their associated theories—local set theories. In the section `Models of First-Order Languages in Categories’ the idea of an interpretation of a many-sorted first-order language is introduced, along with the concept of generic model of a theory formulated in such a language. The chapter concludes with the section `Models in Toposes’, wherein is introduced the concept of a first-order geometric theory and its associated classifying topos containing a generic model of the theory.
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23

Hasegawa, Masahito. Models of Sharing Graphs: A Categorical Semantics of let and letrec. Brand: Springer, 2011.

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24

Models of Sharing Graphs: A Categorical Semantics of let and letrec. Springer, 2011.

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25

Hendriks, Herman. Studied Flexibility. Categories and Types in Syntax and Semantics. ILLC 1993. (ILLC Dissertation Series 1993-5), 1993.

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26

Categorial Investigations: Logical and Linguistic Aspects of the Lambek Calculus. de Gruyter GmbH, Walter, 1988.

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27

Moortgat, Michael. Categorial Investigations: Logical and Linguistic Aspects of the Lambek Calculus. de Gruyter GmbH, Walter, 2020.

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28

Moortgat, Michael. Categorial Investigations: Logical and Linguistic Aspects of the Lambek Calculus. de Gruyter GmbH, Walter, 1991.

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29

Yuasa, Etsuyo. Modularity in Language: Constructional and Categorial Mismatch in Syntax and Semantics. De Gruyter, Inc., 2009.

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30

Yuasa, Etsuyo. Modularity in Language: Constructional and Categorial Mismatch in Syntax and Semantics. De Gruyter, Inc., 2014.

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31

Button, Tim, and Sean Walsh. Categoricity and the natural numbers. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198790396.003.0007.

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This chapter focuses on modelists who want to pin down the isomorphism type of the natural numbers. This aim immediately runs into two technical barriers: the Compactness Theorem and the Löwenheim-Skolem Theorem (the latter is proven in the appendix to this chapter). These results show that no first-order theory with an infinite model can be categorical; all such theories have non-standard models. Other logics, such as second-order logic with its full semantics, are not so expressively limited. Indeed, Dedekind's Categoricity Theorem tells us that all full models of the Peano axioms are isomorphic. However, it is a subtle philosophical question, whether one is entitled to invoke the full semantics for second-order logic — there are at least four distinct attitudes which one can adopt to these categoricity result — but moderate modelists are unable to invoke the full semantics, or indeed any other logic with a categorical theory of arithmetic.
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32

Retore, Christian, and Richard Moot. The Logic of Categorial Grammars: A deductive account of natural language syntax and semantics. Springer, 2012.

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33

Retore, Christian, and Richard Moot. The Logic of Categorial Grammars: A deductive account of natural language syntax and semantics. Springer, 2012.

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34

Halvorson, Hans, and Dimitris Tsementzis. Categories of Scientific Theories. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198748991.003.0017.

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We discuss ways in which category theory might be useful in philosophy of science, in particular for articulating the structure of scientific theories. We argue, moreover, that a categorical approach transcends the syntax–semantics dichotomy in twentieth century analytic philosophy of science.
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35

Cockett, J. R. B., and R. A. G. Seely. Proof Theory of the Cut Rule. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198748991.003.0010.

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This chapter describes the categorical proof theory of the cut rule, a very basic component of any sequent-style presentation of a logic, assuming a minimum of structural rules and connectives, in fact, starting with none. It is shown how logical features can be added to this basic logic in a modular fashion, at each stage showing the appropriate corresponding categorical semantics of the proof theory, starting with multicategories, and moving to linearly distributive categories and *-autonomous categories. A key tool is the use of graphical representations of proofs (“proof circuits”) to represent formal derivations in these logics. This is a powerful symbolism, which on the one hand is a formal mathematical language, but crucially, at the same time, has an intuitive graphical representation.
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36

Jäger, Gerhard. Anaphora and Type Logical Grammar (Trends in Logic). Springer, 2005.

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37

Arka, I. Wayan, Ash Asudeh, and Tracy Holloway King, eds. Modular Design of Grammar. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780192844842.001.0001.

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Modular design of grammar: Linguistics on the edge presents the cutting edge of research on linguistic modules and interfaces in Lexical-Functional Grammar (LFG). LFG has a highly modular design that models the linguistic system as a set of discreet submodules that include, among others, constituent structure, functional structure, argument structure, semantic structure, and prosodic structure, with each module having its coherent properties and being related to each other by correspondence functions. Following a detailed introduction, Part I scrutinises the nature of linguistic structures, interfaces and representations in LFG’s architecture and ontology. Parts II and III are concerned with problems, analyses and generalisations associated with linguistic phenomena which are of long-standing theoretical significance, including agreement, reciprocals, possessives, reflexives, raising, subjecthood, and relativisation, demonstrating how these phenomena can be naturally accounted for within LFG’s modular architecture. Part IV explores issues of the synchronic and diachronic dynamics of syntactic categories in grammar, such as unlike category coordination, fuzzy categorial edges, and consequences of decategorialization, providing explicit LFG solutions to such problems including those which result from language change in progress. The final part re-examines and refines the precise representations and interfaces of syntax with morphology, semantics and pragmatics to account for challenging facts such as suspended affixation, prosody in multiple question word interrogatives and information structure, anaphoric dependencies, and idioms.
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38

Fonteyn, Lauren. Categoriality in Language Change. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780190917579.001.0001.

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This study presents the first elaborate attempt to set out a functional-semantic definition of diachronic transcategorial shift between the major classes “noun”/“nominal” and “verb”/“clause.” In English, speakers have different options to refer to an event by using “deverbal nominalization” strategies (e.g., Him guessing her size/His guessing of her size (was incredibly lucky)). Interestingly, not only do these strategies each resemble “prototypical” nominals to varying extents, it also has been observed that some of these strategies increasingly resemble clauses and decreasingly resemble prototypical nominals over time, as if they are gradually shifting categories. Thus far, the literature on such cases of diachronic categorial shift has mainly described the processes by focusing on form, leaving the reader with a clear picture of what and how changes have occurred. Yet, the question of why these formal changes have occurred is still shrouded in mystery. This study tackles this mystery by showing that the diachronic processes of nominalization and verbalization can also involve functional-semantic changes. The aim of this study is both theoretical and descriptive. The theoretical aim is to present a model that allows one to study diachronic nominalization and verbalization as not just formal or morpho-syntactic but also functional-semantic processes. The descriptive aim is to offer “workable” definitions of the abstract functional-semantic properties of nominals and verbs/clauses, and subsequently apply them to one of the most intriguing deverbal nominalization systems in the history of English: the English gerund.
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39

Aspects of a Theory of Singular Reference: Prolegomena to a Dialectical Logic of Singular Terms. Taylor & Francis Group, 2019.

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40

Greenberg, William J. Aspects of a Theory of Singular Reference. Taylor & Francis Group, 2021.

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41

Greenberg, William J. Aspects of a Theory of Singular Reference: Prolegomena to a Dialectical Logic of Singular Terms. Taylor & Francis Group, 2019.

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42

J, Cresswell M. Logics and Languages. Taylor & Francis Group, 2016.

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43

Caramello, Olivia. Topos-theoretic background. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198758914.003.0003.

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This chapter provides the topos-theoretic background necessary for understanding the contents of the book; the presentation is self-contained and only assumes a basic familiarity with the language of category theory. The chapter begins by reviewing the basic theory of Grothendieck toposes, including the fundamental equivalence between geometric morphisms and flat functors. Then it presents the notion of first-order theory and the various deductive systems for fragments of first-order logic that will be considered in the course of the book, notably including that of geometric logic. Further, it discusses categorical semantics, i.e. the interpretation of first-order theories in categories possessing ‘enough’ structure. Lastly, the key concept of syntactic category of a first-order theory is reviewed; this notion will be used in Chapter 2 for constructing classifying toposes of geometric theories.
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44

Caramello, Olivia. Some Applications. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198758914.003.0012.

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This chapter describes some applications of the theory developed in the previous chapters in a variety of different mathematical contexts. The main methodology used to generate such applications is the ‘bridge technique’ presented in Chapter 2. The discussed topics include restrictions of Morita equivalences to quotients of the two theories involved, give a solution to a prozblem of Lawvere concerning the boundary operator on subtoposes, establish syntax-semantics ‘bridges’ for quotients of theories of presheaf type, present topos-theoretic interpretations and generalizations of Fraïssé’s theorem in model theory on countably categorical theories and of topological Galois theory, develop a notion of maximal spectrum of a commutative ring with unit and investigate compactness conditions for geometric theories allowing one to identify theories lying in smaller fragments of geometric logic.
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45

Pustet, Regina. Copulas: Universals in the Categorization of the Lexicon (Oxford Studies in Typology and Linguistic Theory). Oxford University Press, USA, 2003.

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46

Francis, Elaine J. Gradient Acceptability and Linguistic Theory. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780192898944.001.0001.

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In Gradient Acceptability and Linguistic Theory, Elaine J. Francis examines a challenging problem at the intersection of theoretical linguistics and the psychology of language: the problem of interpreting gradient judgments of sentence acceptability in relation to theories of grammatical knowledge. This problem is important because acceptability judgments constitute the primary source of data on which such theories have been built, despite being susceptible to various extra-grammatical factors. Through a review of experimental and corpus-based research on a variety of syntactic phenomena and an in-depth examination of two case studies, Francis argues for two main positions. The first is that converging evidence from online comprehension tasks, elicited production tasks, and corpora of naturally occurring discourse can help determine the sources of variation in acceptability judgments and narrow down the range of plausible theoretical interpretations. The second is that the interpretation of judgment data depends crucially on one’s theoretical commitments and assumptions, especially with respect to the nature of the syntax–semantics interface and the choice of either a categorical or a gradient notion of grammaticality. The theoretical frameworks considered in this book include derivational theories (e.g. Minimalism, Principles and Parameters), constraint-based theories (e.g. Sign-Based Construction Grammar, Simpler Syntax), competition-based theories (e.g. Stochastic Optimality Theory, Decathlon Model), and usage-based approaches. While showing that acceptability judgment data are typically compatible with the assumptions of various theoretical frameworks, Francis argues that some gradient phenomena are best captured within frameworks that permit soft constraints—non-categorical grammatical constraints that encode the conventional preferences of language users.
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47

Copulas: Universals in the Categorization of the Lexicon (Oxford Studies in Typology and Linguistic Theory). Oxford University Press, USA, 2005.

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48

J, Cresswell M. Logics and Languages. Taylor & Francis Group, 2016.

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49

Logics and Languages. Taylor & Francis Group, 2016.

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