Glue semantics is a theory of the syntax–semantics interface according to which the syntactic structure of a sentence produces premises in a fragment of linear logic, and the semantic interpretation of the sentence correspond to the proof derivable from those premises. This paper describes how Glue can be connected to a Minimalist syntactic theory and compares the result with the more mainstream approach to the syntax–semantics interface in Minimalism, according to which the input to semantic interpretation is (...) a syntactic structure derived by covert movement operations. I argue that the Glue approach has advantages that make it worth exploring. (shrink)

Although ‘glue semantics’ is the most extensively developed theory of semantic composition for LFG, it is not very well integrated into the LFG projection architecture, due to the absence of a simple and well-explained correspondence between glue-proofs and f-structures. In this paper I will show that we can improve this situation with two steps: (1) Replace the current quantificational formulations of glue (either Girard’s system F, or first order linear logic) with strictly propositional linear logic (...) (the quantifier, unit and exponential free version of either MILL or ILL, depending on whether or not tensors are used). (2) Reverse the direction of the standard σ-projection from f-structure to meaning, giving one going from the (atomic nodes of) the glue-proof to the f-structure, rather than from the f-structure to a ‘semantic projection’ which is itself somehow related to the glue-proof. As a side effect, the standard semantic projection of LFG glue semantics can be dispensed with. A result is that LFG sentence structures acquire a level composed of strictly binary trees, constructed out of nodes representing function application and lambda abstraction, with a significant resemblance to external and internal merge in the Minimalist Program. This increased resemblance between frameworks might assist in making useful comparisons. (shrink)

The glueing of (sequentially, pointwise, or uniformly) continuous functions that coincide on the intersection of their closed domains is examined in the light of Bishop-style constructive analysis. This requires us to pay attention to the way that the two domains intersect.

Glue has evolved significantly during the past decade. Although the recent move to type-theoretic notation was a step in the right direction, basing the current Glue system on System F (second-order λ-calculus) was an unfortunate choice. An extension to two sorts and ad hoc restrictions were necessary to avoid inappropriate composition of meanings. As a result, the current system is unnecessarily complicated. A first-order Glue system is hereby proposed as its replacement. This new system is not only (...) simpler and more elegant, as it captures the exact requirements for Glue-style compositionality without ad hoc improvisations, but it also turns out to be more powerful than the current two-sorted (pseudo-) second-order system. First-order Glue supports all existing Glue analyses as well as more elegant alternatives. It also supports new, more demanding analyses. (shrink)

’s glue logic for computing logical form dynamic. This allows us to model a dialogue agent’s understanding of what the update of the semantic representation of the dialogue would be after his next contribution, including the effects of the rhetorical moves that he is contemplating performing next. This is a pre-requisite for developing a model of how agents reason about what to say next. We make the glue logic dynamic by using a dynamic public announcement (...) class='Hi'>logic ( pal ). We extend pal with a particular variety of default reasoning suited to reasoning about discourse—this default reasoning being an essential component of inferring the pragmatic effects of one’s dialogue moves. We add to the pal language a new type of announcement, known as ceteris paribus announcement, and this is used to model how an agent anticipates the (default) pragmatic effects of his next dialogue move. Our extended pal validates certain intuitive patterns of default inference that existing pal s for practical reasoning do not. We prove that the dynamic glue logic has a pspace validity problem, and as such is no more complex than pal with multiple $${\square}$$ operators. (shrink)

I read Stefan Collini’s What are Universities For? last week with very mixed feelings. In the past, I’ve much admired his polemical essays on the REF, “impact”, the Browne Report, etc. in the London Review of Books and elsewhere: they speak to my heart. If you don’t know those essays, you can get some of their flavour from his latest article in the Guardian yesterday. But I found the book a disappointment. Perhaps the trouble is that Collini is too decent, (...) too high-minded, has too unrealistically exalted a view about what actually happens in universities which is too coloured by attitudes appropriate to the traditional humanities. And he is optimistic to the point of fantasy if he thinks that people are so susceptible to “the romance of ideas and the power of beauty” that they will want, or can be brought to want, lots and lots of universities in order to promote the ideas (as if they would suppose that the task of “conserving, understanding, extending and handing on to subsequent generations the intellectual, scientific, and artistic heritage of mankind” was clearly ill-served when there were only forty universities in England, as opposed to a hundred and whatever). (shrink)

A common reaction to Hegel’s suggestion that we collapse Kant’s distinction between form and content is that, since such a move would also deprive us of any way of distinguishing the merely logical from the real possibility of our concepts, it is incoherent and ought to be rejected. It is true that these two distinctions are intimately related in Kant, such that if one goes, the other does as well. But it is less obvious that giving them up as Kant (...) conceives them is as incoherent a proposal as many of Hegel’s critics think. It has been the point of a recent account of Hegel’s idealism to demonstrate that his critique of Kant’s dichotomy between form and content or concept and intuition does not commit him to the view that human cognition is materially creative of its content in the manner of a God-like or intuitive intellect—does not, in other words, signify a return to a pre-Critical metaphysics. This is the interpretative stance I adopt here as well, in hope of giving defenders of Kant reasons for taking Hegel more seriously. (shrink)