Hybrid type theory: a quartet in four movements

This paper sings a song -a song created by bringing together the work of four great names in the history of logic: Hans Reichenbach, Arthur Prior, Richard Montague, and Leon Henkin. Although the work of the first three of these authors have previously been combined, adding the ideas of Leon Henkin is the addition required to make the combination work at the logical level. But the present paper does not focus on the underlying technicalities (these can be found in Areces, Blackburn, Huertas, and Manzano [to appear]) rather it focusses on the underlying instruments, and the way they work together. We hope the reader will be tempted to sing along

Treating Coordination with Datalog Grammars

In previous work we studied a new type of DCGs, Datalog grammars, which are inspired on database theory. Their efficiency was shown to be better than that of their DCG counterparts under (terminating) OLDT-resolution. In this article we motivate a variant of Datalog grammars which allows us a meta-grammatical treatment of coordination. This treatment improves in some respects over previous work on coordination in logic grammars, although more research is needed for testing it in other respects

Sloppy Identity

Although sloppy interpretation is usually accounted for by theories of ellipsis, it often arises in non-elliptical contexts. In this paper, a theory of sloppy interpretation is provided which captures this fact. The underlying idea is that sloppy interpretation results from a semantic constraint on parallel structures and the theory is shown to predict sloppy readings for deaccented and paycheck sentences as well as relational-, event-, and one-anaphora. It is further shown to capture the interaction of sloppy/strict ambiguity with quantification and binding.Comment: 20 page

WARP: Weight Associative Rule Processor. A dedicated VLSI fuzzy logic megacell

During the last five years Fuzzy Logic has gained enormous popularity in the academic and industrial worlds. The success of this new methodology has led the microelectronics industry to create a new class of machines, called Fuzzy Machines, to overcome the limitations of traditional computing systems when utilized as Fuzzy Systems. This paper gives an overview of the methods by which Fuzzy Logic data structures are represented in the machines (each with its own advantages and inefficiencies). Next, the paper introduces WARP (Weight Associative Rule Processor) which is a dedicated VLSI megacell allowing the realization of a fuzzy controller suitable for a wide range of applications. WARP represents an innovative approach to VLSI Fuzzy controllers by utilizing different types of data structures for characterizing the membership functions during the various stages of the Fuzzy processing. WARP dedicated architecture has been designed in order to achieve high performance by exploiting the computational advantages offered by the different data representations

Mathematical Foundations for a Compositional Distributional Model of Meaning

We propose a mathematical framework for a unification of the distributional theory of meaning in terms of vector space models, and a compositional theory for grammatical types, for which we rely on the algebra of Pregroups, introduced by Lambek. This mathematical framework enables us to compute the meaning of a well-typed sentence from the meanings of its constituents. Concretely, the type reductions of Pregroups are `lifted' to morphisms in a category, a procedure that transforms meanings of constituents into a meaning of the (well-typed) whole. Importantly, meanings of whole sentences live in a single space, independent of the grammatical structure of the sentence. Hence the inner-product can be used to compare meanings of arbitrary sentences, as it is for comparing the meanings of words in the distributional model. The mathematical structure we employ admits a purely diagrammatic calculus which exposes how the information flows between the words in a sentence in order to make up the meaning of the whole sentence. A variation of our `categorical model' which involves constraining the scalars of the vector spaces to the semiring of Booleans results in a Montague-style Boolean-valued semantics.Comment: to appea

P-model Alternative to the T-model

Standard linguistic analysis of syntax uses the T-model. This model requires the ordering: D-structure $>$ S-structure $>$ LF, where D-structure is the deep structure, S-structure is the surface structure, and LF is logical form. Between each of these representations there is movement which alters the order of the constituent words; movement is achieved using the principles and parameters of syntactic theory. Psychological analysis of sentence production is usually either serial or connectionist. Psychological serial models do not accommodate the T-model immediately so that here a new model called the P-model is introduced. The P-model is different from previous linguistic and psychological models. Here it is argued that the LF representation should be replaced by a variant of Frege's three qualities (sense, reference, and force), called the Frege representation or F-representation. In the F-representation the order of elements is not necessarily the same as that in LF and it is suggested that the correct ordering is: F-representation $>$ D-structure $>$ S-structure. This ordering appears to lead to a more natural view of sentence production and processing. Within this framework movement originates as the outcome of emphasis applied to the sentence. The requirement that the F-representation precedes the D-structure needs a picture of the particular principles and parameters which pertain to movement of words between representations. In general this would imply that there is a preferred or optimal ordering of the symbolic string in the F-representation. The standard ordering is retained because the general way of producing such an optimal ordering is unclear. In this case it is possible to produce an analysis of movement between LF and D-structure similar to the usual analysis of movement between S-structure and LF. It is suggested that a maximal amount of information about a language's grammar and lexicon is stored, because of the necessity of analyzing corrupted data