Logical aspects of computational linguistics

2016

Reviewed by Francesco-Alessio Ursini, Stockholms Universitet The Modular Architecture of Grammar presents a state-of-the-art introduction to automodular grammar, a theory based on Fodor's (1983) modularity of mind hypothesis. According to the Modularity of Grammar Hypothesis, autonomous modules generate linguistic representations (e.g. sentence structures, propositions), but do not interact (p.7). The representations that these systems generate, however, are connected via mapping principles governed by the interface (meta-)module. The theoretical consequences of this assumption are far-reaching. For instance, the theory lacks movement operations or hierarchical levels of representation, and syntax does not have a central function in the architecture (cf. GB and Distributed Morphology: Chomsky 1981, Halle & Marantz 1993). The theory is tested against a wide set of data, including some well-known but still controversial problems. It presents an interesting representational alternative to derivational theories, and can provide several stimulating points of reflection for theoretically-inclined linguists. Below, I summarize the contents of the book. Chapter 1 introduces the two central modules of this architecture: semantics and syntax. The semantic module generates Function/Argument (FA) structures, which determine how the meanings of lexical items, phrases and sentences are composed. The syntax module generates phrase/sentence structure, as standardly assumed in generative frameworks. The syntactic rules of representation come in a standard, if conservative generative format (e.g. S→NP, VP). The semantic rules also come in a conservative, categorial format. For instance, an object of type Fap is a function that takes an argument object of type a as an input, and returns a type p proposition as a result (cf. Cresswell 1973). Lexical items are initially defined as pairings of F/A and syntactic representations, which include information about category and distribution. For instance, the intransitive verb sneeze has F/A type Fa and syntactic category "V in [VP ___]" (i.e. it is a verb in a VP). Chapter 2 presents the interface module and its three core principles. The first is lexical correspondence: each lexical item must have a representation in each module/dimension. The second is categorial correspondence: categories from different modules are mapped in a homogenous way (e.g. NPs to arguments, propositions to sentences). The third is geometric correspondence: relations from one dimension (e.g. c-command in syntax) must correspond to relation in another dimension (e.g. scope in semantics). Since the theory assumes that different rules generate syntactic and semantic representations, which are however connected via precise mappings, it predicts that discrepancies and asymmetries among representations can arise. For instance, copular sentences such as Sally is a carpenter are analysed as including lexical correspondence discrepancies. The copula and indefinite article are treated as having null semantic representations, the NPs Sally and carpenter as having semantic representations that combine to form a proposition (i.e. argument for Sally, predicate for carpenter). The interface module maps these NPs to respectively argument and predicate type representations, and copula and indefinite article to null representations. Hence, lexical and categorial correspondence are maintained even if not all syntactic representations correspond to non-null semantic representations. Chapter 3 adds the role (also event, cognitive) structure module, which determines the event structure and thematic roles associated to lexical items and sentences. Only three roles are postulated: proto-agent, proto-patient, and ancillary participant (cf. Dowty 1991). Thus, the role structure of a verb such as put can be represented as "RS: "put" (type), AGT, PAT, ANC". Notably, role structures are assumed to be "flat" sequences including event type and roles. The assumption of a distinct role structure module is motivated via the analysis of voice

Published originally as "Loogisen kielentutkimuksen näköaloja", Ajatus 19, (1956), pp. 81-96, the following piece by Jaakko Hintikka is the first essay he published in his mother tongue of Finnish. It is seen to provide both a state-of-the-art review of current topics emerging in the philosophy of language in the mid-1950, as well as outlines of Hintikka's own evaluation of major theses of that era, in particular those of Quine's and Wittgenstein's concerning language use. Hintikka evaluates contributions that the logical study of language use can make to the solving of philosophical questions. Published in 1956 in Ajatus: The Yearbook of the Philosophical Society of Finland, Hintikka's essay served to introduce these topical issues to the Finnish-speaking audience soon after the original works had appeared in print. It also puts the theses into the perspectives of Hintikka's own fledgling logical philosophy. One can see the germs of game-theoretical semantics is his comments on Wittgenstein's notion of a language-game, and his remarks on general habits of action anticipate the importance of strategic rules in Hintikka's mature, inquiry-led and 'action-first' epistemology. This is manifest in Hintikka's characteristic approach to the methodology of philosophy of science and mathematics as an attempt to understand the nature of scientific and mathematical practices and operations through the logical analysis of their central concepts. Topics indicated below thus became the hallmarks of Hintikka's next sixty years of work, which saw the development of a range of logical methods by which language and its use can be studied, and in particular in such a way that progress can be made in solving problems of genuinely philosophical nature that one encounters across various fields of science. This piece was very briefly summarized in English in 1963 by Arto Salomaa (The Journal of Symbolic Logic 28(2), 1963, p. 165), and it is translated from the original Finnish by Jukka Nikulainen and Ahti-Veikko Pietarinen.

2000

Higginbotham and May (1981), Higginbotham (1985), and May (1985), (1989), and (1991), have the Fregeen view within the framework of Chomsky's Principles and Parameters model of grammar. 2 They propose a rule of quantifier raising (QR) which adjoins quantified NPs to VP or IP. This rule creates an abstract (non-overt) level of syntactic slructure, logical form (LF), in which a

Journal of Logic, Language and Information, 2004

Even though residuation is at the core of Categorial Grammar [11], it is not always immediate to realize how standard logic systems like Multi-modal Categorial Type Logics (MCTL) [17] actually embody this property. In this paper we focus on the basic system NL [12] and its extension with unary modalities NL(3) [16], and we spell things out by means of Display Calculi (DC) [3, 10]. The use of structural operators in DC permits a sharp distinction between the core properties we want to impose on the logic system and the way these properties are projected into the logic operators. We will show how we can obtain Lambek residuated triple \, / and • of binary operators, and how the operators 3 and 2 ↓ introduced by Moortgat in [16] are indeed their unary counterpart. In the second part of the paper we turn to other important algebraic properties which are usually investigated in conjunction with residuation [5]: Galois and dual Galois connections. Again, DC let us readily define logic calculi capturing them, and we will discuss different possibilities in which the logic operators so obtained can interact with those obtained from residuation. We also provide preliminary ideas on how to use them when modeling linguistic phenomena.

Logic, Language, Information, and Computation, 2019

This paper proposes an analysis of modal auxiliaries in English in Type-Logical Grammar. The proposed analysis captures the scopal interactions between different types of modal auxiliaries and negation by incorporating the key analytic idea of Iatridou and Zeijlstra [6], who classify English modal auxiliaries into PPI and NPI types. In order to technically implement this analysis, we build on Kubota and Levine's [8, 10] treatment of modal auxiliaries as higher-order operators that take scope at the clausal level. The proposed extension of the Kubota/Levine analysis is shown to have several interesting consequences, including a formal derivability relation from the higher-order entry for auxiliaries to a lowerorder VP/VP entry traditionally recognized in categorial grammar (CG) research. The systematic analysis of the scopal properties of auxiliaries and the somewhat more abstract meta-comparison between 'transformational' and 'non-transformational' analytic ideas that become possible in a typelogical setup highlight the value of taking a logical perspective on the syntax of natural language embodied in Type-Logical Grammar research.