We design new languages, by and large, in order to bypass complexities and limitations within the languages we already have. But when we are concerned with language itself we should guard against projecting the simple and powerful syntax and semantics we have concocted back into the sentences we encounter. For some of the features of English, French, or Ancient Greek we routinely abstract away from in the process of formalization might be linguistic universals – the very features that set human (...) languages apart from all the other conceivable ones. How similar natural languages really are to formal ones is an empirical question for linguistics. (shrink)

This is the first part of a two-part article on semantic compositionality, that is, the principle that the meaning of a complex expression is determined by the meanings of its parts and the way they are put together. Here we provide a brief historical background, a formal framework for syntax and semantics, precise definitions, and a survey of variants of compositionality. Stronger and weaker forms are distinguished, as well as generalized forms that cover extra-linguistic context dependence as well as linguistic (...) context dependence. In the second article, we survey arguments for and arguments against the claim that natural languages are compositional, and consider some problem cases. It will be referred to as Part II. (shrink)

This paper attempts to describe and address a specific puzzle related to compositionality in artificial networks such as Deep Neural Networks and machine learning in general. The puzzle identified here touches on a larger debate in Artificial Intelligence related to epistemic opacity but specifically focuses on computational applications of human level linguistic abilities or properties and a special difficulty with relation to these. Thus, the resulting issue is both general and unique. A partial solution is suggested.

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 investigates relative constructions as in The gifted mathematician that you claim to be should be able to solve this equation, in which the head noun is semantically dependent on an intensional operator in the relative clause, even though it is not c-commanded by it. This is the kind of situation that has led, within models of linguistic description that assume a syntactic level of Logical Form, to analyses in which the head noun is interpreted within the CP-internal gap (...) by reconstruction or interpretation of a lower element of a chain. We offer a solution that views surface representation as the input to semantics. The apparent inverted scope effects are traced back to the interpretation of the head nominal gifted mathematician as applying to individual concepts, and of the relative clause that you claim to be as including an equational statement. According to this view, the complex DP in question refers to the individual concept that exists just in the worlds that are compatible with what is generally supposed to be the case, is a gifted mathematician in those worlds, and is identical to you in those worlds. Our solution is related to the non-reconstructionist analysis of binding of pronouns that do not stand in a c-command relationship to their binder, as in The woman that every man hugged was his mother in Jacobson Proceedings of Semantics and Linguistic Theory IV:161-178, 1994) and Sharvit Proceedings of Semantics and Linguistic Theory VI:227-244, 1996), and allows us to capture both similarities with and differences from the latter type of construction. We point out and offer explanations for a number of properties of such relative clauses—in particular their need for an internal intensional operator, their incompatibility with any determiner other than the definite article, and the fact that some of their properties are shared by demonstrably distinct kinds of relative clauses. (shrink)

This paper presents a variable-free analysis of relational nouns in Glue Semantics, within a Lexical Functional Grammar (LFG) architecture. Relational nouns and resumptive pronouns are bound using the usual binding mechanisms of LFG. Special attention is paid to the bound readings of relational nouns, how these interact with genitives and obliques, and their behaviour with respect to scope, crossover and reconstruction. I consider a puzzle that arises regarding relational nouns and resumptive pronouns, given that relational nouns can have bound readings (...) and resumptive pronouns are just a specific instance of bound pronouns. The puzzle is why is it impossible for bound implicit arguments of relational nouns to be resumptive? The puzzle is highlighted by a well-known variety of variable-free semantics, where pronouns and relational noun phrases are identical both in category and (base) type. I show that the puzzle also arises for an established variable-based theory. I present an analysis of resumptive pronouns that crucially treats resumptives in terms of the resource logic linear logic that underlies Glue Semantics: a resumptive pronoun is a perfectly ordinary pronoun that constitutes a surplus resource; this surplus resource requires the presence of a resumptive-licensing resource consumer, a manager resource. Manager resources properly distinguish between resumptive pronouns and bound relational nouns based on differences between them at the level of semantic structure. The resumptive puzzle is thus solved. The paper closes by considering the solution in light of the hypothesis of direct compositionality. It is argued that a directly compositional version of the theory is possible, although perhaps not desirable. The implications for direct compositionality are considered. (shrink)

Equational intensional ‘reconstruction’ relatives. Submitted.