This article proposes that predicate order and coherence relations are the two major determining factors in copredication licensing, resolving a long-standing puzzle over the criteria for constructing acceptable copredications. The effects of predicate ordering are claimed to be anchored around semantic complexity, such that copredications with semantically Simple–Complex predicate orderings are more acceptable than the reverse. This motivates a parsing bias, termed Incremental Semantic Complexity. Particular ways of implementing this parsing bias are discussed. The effect of predicate coherence is claimed (...) to be anchored around a sense of causality and featural commonality. Lastly, a hierarchy of possible copredications is outlined (the Copredication Hierarchy), helping to delimit the modelling of copredications to a greater extent than has previously been possible. (shrink)

Abstract The purpose of this paper is twofold: (i) we will argue that formal semantics might have faltered due to its failure in distinguishing between two fundamentally very different types of concepts, namely ontological concepts, that should be types in a strongly-typed ontology, and logical concepts, that are predicates corresponding to properties of, and relations between, objects of various ontological types; and (ii) we show that accounting for these differences amounts to a new formal semantics; one that integrates lexical and (...) compositional semantics in one coherent framework and one where formal semantics is embedded with a strongly typed ontology; an ontology that reflects our commonsense knowledge of the world and the way we talk about it in ordinary language. We will show how in such a framework a number of challenges in the semantics of natural language are adequately and systematically treated. (shrink)

In formal semantics based on modern type theories, some sentences may be interpreted as judgements and some as logical propositions. When interpreting composite sentences, one may want to turn a judgemental interpretation or an ill-typed semantic interpretation into a proposition in order to obtain an intended semantics. For instance, an incorrect judgement $$a:A$$ may be turned into its propositional form $$\textsc {is}(A,a)$$ and an ill-typed application p(a) into $$\textsc {do}(p,a)$$, so that the propositional forms can take part in logical compositions (...) that interpret composite sentences, especially those that involve negations and conditionals.In this paper, we propose an operator not that facilitates such a transformation. Introducing not axiomatically, with five axiomatic laws to govern its behaviour, we shall use it to define $$\textsc {is}$$ and $$\textsc {do}$$ and give examples to illustrate its use in semantic interpretation. The introduction of not into type theories is logically consistent – this is justified by showing that not can be defined by means of the heterogeneous equality $$\textrm{JMeq}$$ so that all of the axiomatic laws for not become provable. Therefore, since the extension with $$\textrm{JMeq}$$ preserves logical consistency, so does the extension with not. We shall also study conditions under which $$\textsc {is}$$ and $$\textsc {do}$$ operators can be used safely without the risk of over-generation. (shrink)

Copredication is the phenomenon whereby two or more predicates seem to require that their argument denotes different things. The denotation of words that copredicate has been broadly discussed. In this paper, I investigate the metaphysics behind this question. Thus, mereological theories of dot objects claim that these nouns denote complex entities; Asher (Lexical meaning in context, Cambridge University Press, 2011, https://doi.org/10.1017/CBO9780511793936) thinks that they denote bare particulars; and the Activation Package Theory contends that they stand for multiple denotations. According to (...) the Activation Package Theory, copredicative nouns stand for complex knowledge structures that offer a range of multiple potential denotations. In this paper, I claim that the Activation Package Theory contributes to solve some of the metaphysical questions that arise from copredication. (shrink)

In this paper we propose a way to deal with natural language inference by implementing Modern Type Theoretical Semantics in the proof assistant Coq. The paper is a first attempt to deal with NLI and natural language reasoning in general by using the proof assistant technology. Valid NLIs are treated as theorems and as such the adequacy of our account is tested by trying to prove them. We use Luo’s Modern Type Theory with coercive subtyping as the formal language into (...) which we translate natural language semantics, and we further implement these semantics in the Coq proof assistant. It is shown that the use of a MTT with an adequate subtyping mechanism can give us a number of promising results as regards NLI. Specifically, it is shown that a number of inference cases, i.e. quantifiers, adjectives, conjoined noun phrases and temporal reference among other things can be successfully dealt with. It is then shown, that even though Coq is an interactive and not an automated theorem prover, automation of all of the test examples is possible by introducing user-defined automated tactics. Lastly, the paper offers a number of innovative approaches to NL phenomena like adjectives, collective predication, comparatives and factive verbs among other things, contributing in this respect to the theoretical study of formal semantics using MTTs. (shrink)

Vector models of language are based on the contextual aspects of words and how they co-occur in text. Truth conditional models focus on the logical aspects of language, the denotations of phrases, and their compositional properties. In the latter approach the denotation of a sentence determines its truth conditions and can be taken to be a truth value, a set of possible worlds, a context change potential, or similar. In this short paper, we develop a vector semantics for language based (...) on the simply typed lambda calculus. Our semantics uses techniques familiar from the truth conditional tradition and is based on a form of dynamic interpretation inspired by Heim's context updates. (shrink)

In this paper we present a study of adjectival/adverbial modification using modern type theories, i.e. type theories within the tradition of Martin-Löf. We present an account of various issues concerning adjectival/adverbial modification and argue that MTTs can be used as an adequate language for interpreting NL semantics. MTTs are not only expressive enough to deal with a range of modification phenomena, but are furthermore well-suited to perform reasoning tasks that can be easily implemented given their proof-theoretic nature. In MTT-semantics, common (...) nouns are interpreted as types rather than predicates. Therefore, in order to capture the semantics of adjectives adequately, one needs to meet the challenge of modeling CNs modified by adjectives as types. To explicate that this can be done successfully, we first look at the mainstream classification of adjectives, i.e. intersective, subsective and non-subsective adjectives. There, we show that the rich type structure available in MTTs, along with a suitable subtyping framework, offers an adequate mechanism to model these cases. In particular, this modelling naturally takes care of the characterising inferences associated with each class of adjectives. Then, more advanced issues on adjectival modification are discussed: degree adjectives, comparatives and multidimensional adjectives. There, it is shown that the use of indexed types can be usefully applied in order to deal with these cases. In the same vein, the issue of adverbial modification is discussed. We study two general typings for sentence and VP adverbs respectively. It is shown that the rich type structure in MTTs further provides useful organisational mechanisms in giving formal semantics for adverbs. In particular, we discuss the use of \-types to capture the veridicality/non-veridicality distinction and further discuss cases of intensional adverbs using the type theoretic notion of context. We also look at manner, subject and speech act adverbials and propose solutions using MTTs. Finally, we show that the current proof technology can help mechanically check the associated inferences. A number of our proposals concerning adjectival and adverbial modification have been formalised in the proof assistant Coq and many of the associated inference patterns are checked to be correctly captured. (shrink)

In this paper I focus on a recently discussed phenomenon illustrated by sentences containing predicates of taste: the phenomenon of " perspectival plurality " , whereby sentences containing two or more predicates of taste have readings according to which each predicate pertains to a different perspective. This phenomenon has been shown to be problematic for (at least certain versions of) relativism. My main aim is to further the discussion by showing that the phenomenon extends to other perspectival expressions than predicates (...) of taste and by proposing a general solution to the problem raised by it on behalf of the relativist. The core claim of the solution (" multiple indexing ") is that utterances of sentences containing perspectival expressions should be evaluated with respect to (possibly infinite) sequences of perspective parameters. (shrink)

The paper develops a proof-theoretic semantics for belief reports by extending the constructive type-theoretical formalism presented in Więckowski with a specific kind of set-forming operator suited for the representation of belief attitudes. The extended formalism allows us to interpret constructions which involve, e.g., iteration of belief, quantifying into belief contexts, and anaphora in belief reports. Moreover, constructive solutions to canonical instances of the problem of hyperintensionality are suggested. The paper includes a discussion of Ranta’s constructive account of belief reports.

We argue that logical semantics might have faltered due to its failure in distinguishing between two fundamentally very different types of concepts: ontological concepts, that should be types in a strongly-typed ontology, and logical concepts, that are predicates corresponding to properties of and relations between objects of various ontological types. We will then show that accounting for these differences amounts to the integration of lexical and compositional semantics in one coherent framework, and to an embedding in our logical semantics of (...) a strongly-typed ontology that reflects our commonsense view of the world and the way we talk about it in ordinary language. We will show that in such a framework a number of challenges in natural language semantics can be adequately and systematically treated. (shrink)

In this paper, we investigate the possibility of translating a fragment of natural deduction system (NDS) for natural language semantics into modern type theory (MTT), originally suggested by Luo (2014). Our main goal will be to examine and translate the basic rules of NDS (namely, meta-rules, structural rules, identity rules, noun rules and rules for intersective and subsective adjectives) to MTT. Additionally, we will also consider some of their general features.

This paper proposes a unified dependent type analysis of three puzzling phenomena: inversely linked interpretations, weak definite readings in possessives and Haddock-type readings. We argue that the three problematic readings have the same underlying surface structure, and that the surface structure postulated can be interpreted properly and compositionally using dependent types. The dependent type account proposed is the first, to the best of our knowledge, to formally connect the three phenomena. A further advantage of our proposal over previous analyses is (...) that it offers a principled solution to the puzzle of why both inversely linked interpretations and weak definite readings are blocked with certain prepositions. (shrink)

This paper is a reflexion on the computability of natural language semantics. It does not contain a new model or new results in the formal semantics of natural language: it is rather a computational analysis, in the context for type-logical grammars, of the logical models and algorithms currently used in natural language semantics, defined as a function from a grammatical sentence to a set of logical formulas—because a statement can be ambiguous, it can correspond to multiple formulas, one for each (...) reading. We argue that as long as we do not explicitly compute the interpretation in terms of possible world models, one can compute the semantic representation of a given statement, including aspects of lexical meaning. This is a very generic process, so the results are, at least in principle, widely applicable. We also discuss the algorithmic complexity of this process. (shrink)

This paper provides a detailed comparison between discourse representation theory and dependent type semantics, two frameworks for discourse semantics. Although it is often stated that DRT and those frameworks based on dependent types are mutually exchangeable, we argue that they differ with respect to variable handling, more specifically, how substitution and other operations on variables are defined. This manifests itself in two recalcitrant problems posed for DRT; namely, the overwrite problem and the duplication problem. We will see that these problems (...) still pose a challenge for various extended compositional systems based on DRT, while they do not arise in a framework of DTS where substitution and other operations are defined in the standard type-theoretic manner without stipulating any additional constraints. We also compare the notions of contexts underlying these two kinds of frameworks, namely, contexts represented as assignment functions and contexts represented as proof terms, and see what different predictions they make for some linguistic examples. (shrink)

The paper proposes a new semantics with dependent types for indefinites, encompassing both the data related to their exceptional scopal behavior and the data related to their anaphoric properties. The proposal builds on the formal system combining generalized quantifiers with dependent types in [Grudzińska & Zawadowski 2014] and [Grudzińska & Zawadowski 2016].