Type-driven semantic interpretation and feature dependencies in R-LFG

Once one has enriched LFG's formal machinery with the linear logic mechanisms needed for semantic interpretation as proposed by Dalrymple et. al., it is natural to ask whether these make any existing components of LFG redundant. As Dalrymple and her colleagues note, LFG's f-structure completeness and coherence constraints fall out as a by-product of the linear logic machinery they propose for semantic interpretation, thus making those f-structure mechanisms redundant. Given that linear logic machinery or something like it is independently needed for semantic interpretation, it seems reasonable to explore the extent to which it is capable of handling feature structure constraints as well. R-LFG represents the extreme position that all linguistically required feature structure dependencies can be captured by the resource-accounting machinery of a linear or similiar logic independently needed for semantic interpretation, making LFG's unification machinery redundant. The goal is to show that LFG linguistic analyses can be expressed as clearly and perspicuously using the smaller set of mechanisms of R-LFG as they can using the much larger set of unification-based mechanisms in LFG: if this is the case then we will have shown that positing these extra f-structure mechanisms is not linguistically warranted.Comment: 30 pages, to appear in the the ``Glue Language'' volume edited by Dalrymple, uses tree-dvips, ipa, epic, eepic, fullnam

Comparing and evaluating extended Lambek calculi

Lambeks Syntactic Calculus, commonly referred to as the Lambek calculus, was innovative in many ways, notably as a precursor of linear logic. But it also showed that we could treat our grammatical framework as a logic (as opposed to a logical theory). However, though it was successful in giving at least a basic treatment of many linguistic phenomena, it was also clear that a slightly more expressive logical calculus was needed for many other cases. Therefore, many extensions and variants of the Lambek calculus have been proposed, since the eighties and up until the present day. As a result, there is now a large class of calculi, each with its own empirical successes and theoretical results, but also each with its own logical primitives. This raises the question: how do we compare and evaluate these different logical formalisms? To answer this question, I present two unifying frameworks for these extended Lambek calculi. Both are proof net calculi with graph contraction criteria. The first calculus is a very general system: you specify the structure of your sequents and it gives you the connectives and contractions which correspond to it. The calculus can be extended with structural rules, which translate directly into graph rewrite rules. The second calculus is first-order (multiplicative intuitionistic) linear logic, which turns out to have several other, independently proposed extensions of the Lambek calculus as fragments. I will illustrate the use of each calculus in building bridges between analyses proposed in different frameworks, in highlighting differences and in helping to identify problems.Comment: Empirical advances in categorial grammars, Aug 2015, Barcelona, Spain. 201

The price of inscrutability

In our reasoning we depend on the stability of language, the fact that its signs do not arbitrarily change in meaning from moment to moment.(Campbell, 1994, p.82) Some philosophers offer arguments contending that ordinary names such as “London” are radically indeterminate in reference. The conclusion of such arguments is that there is no fact of the matter whether “London” refers to a city in the south of England, or whether instead it refers to Sydney, Australia. Some philosophers have even suggested that we accept the conclusion of these arguments. Such a position seems crazy to many; but what exactly goes wrong if one adopts such a view? This paper evaluates the theoretical costs incurred by one who endorses extreme inscrutability of reference (the ‘inscrutabilist’). I show that there is one particular implication of extreme inscrutability which pushes the price of inscrutabilism too high. An extension of the classic ‘permutation’ arguments for extreme inscrutability allow us to establish what I dub ‘extreme indexical inscrutability’. This result, I argue, unacceptably undermines the epistemology of inference. The first half of the paper develops the background of permutation arguments for extreme inscrutability of reference and evaluates some initial attempts to make trouble for the inscrutabilist. Sections 1 and 2 describe the setting of the original permutation arguments for extreme inscrutability. Sections 3 and 4 survey four potential objections to extreme inscrutability of reference, including some recently raised in Vann McGee’s excellent (2005a). Sections 5 sketches how the permutation arguments can be generalized to establish extreme indexical inscrutability; and shows how this contradicts a ‘stability principle’—that our words do not arbitrarily change their reference from one moment to the next—which I claim plays a vital role in the epistemology of inference. The second half of the paper develops in detail the case for thinking that language is stable in the relevant sense. In section 6, I use this distinction to call into question the epistemological relevance of validity of argument types; Kaplan’s treatment of indexical validity partially resolves this worry, but there is a residual problem. In section 7, I argue that stability is exactly what is needed to bridge this final gap, and so secure the relevance of validity to good inferential practice. Section 8 responds to objections to this claim. An appendix to the paper provides formal backing for the results cited in this paper, including a generalization of permutation arguments to the kind of rich setting required for a realistic semantics of natural language.1 Extreme indexical inscrutability results can be proved within this setting. The first half of the paper shows that the inscrutabilist is committed to extreme indexical inscrutability, which implies that language not determinately ‘stable’. The second half of the paper argues that good inference requires stability. The price of inscrutabilism, therefore, is to sever the connection between the validity of argument-forms and inferential practice: and this is too high a price to pay