2,896 research outputs found
From compositional to systematic semantics
We prove a theorem stating that any semantics can be encoded as a
compositional semantics, which means that, essentially, the standard definition
of compositionality is formally vacuous. We then show that when compositional
semantics is required to be "systematic" (that is, the meaning function cannot
be arbitrary, but must belong to some class), it is possible to distinguish
between compositional and non-compositional semantics. As a result, we believe
that the paper clarifies the concept of compositionality and opens a
possibility of making systematic formal comparisons of different systems of
grammars.Comment: 11 pp. Latex.
Linguistics and some aspects of its underlying dynamics
In recent years, central components of a new approach to linguistics, the
Minimalist Program (MP) have come closer to physics. Features of the Minimalist
Program, such as the unconstrained nature of recursive Merge, the operation of
the Labeling Algorithm that only operates at the interface of Narrow Syntax
with the Conceptual-Intentional and the Sensory-Motor interfaces, the
difference between pronounced and un-pronounced copies of elements in a
sentence and the build-up of the Fibonacci sequence in the syntactic derivation
of sentence structures, are directly accessible to representation in terms of
algebraic formalism. Although in our scheme linguistic structures are classical
ones, we find that an interesting and productive isomorphism can be established
between the MP structure, algebraic structures and many-body field theory
opening new avenues of inquiry on the dynamics underlying some central aspects
of linguistics.Comment: 17 page
A Graph Rewriting Approach for Transformational Design of Digital Systems
Transformational design integrates design and verification. It combines âcorrectness by constructionâ and design creativity by the use of pre-proven behaviour preserving transformations as design steps. The formal aspects of this methodology are hidden in the transformations. A constraint is the availability of a design representation with a compositional formal semantics. Graph representations are useful design representations because of their visualisation of design information. In this paper graph rewriting theory, as developed in the last twenty years in mathematics, is shown to be a useful basis for a formal framework for transformational design. The semantic aspects of graphs which are no part of graph rewriting theory are included by the use of attributed graphs. The used attribute algebra, table algebra, is a relation algebra derived from database theory. The combination of graph rewriting, table algebra and transformational design is new
Semantic construction in feature-based TAG
We propose a semantic construction method for Feature-Based Tree Adjoining Grammar which is based on the derived tree, compare it with related proposals and briefly discuss some implementation possibilities
Efficient deep processing of japanese
We present a broad coverage Japanese grammar written in the HPSG formalism with MRS semantics. The grammar is created for use in real world applications, such that robustness and performance issues play an important role. It is connected to a POS tagging and word segmentation tool. This grammar is being developed in a multilingual context, requiring MRS structures that are easily comparable across languages
Geometric representations for minimalist grammars
We reformulate minimalist grammars as partial functions on term algebras for
strings and trees. Using filler/role bindings and tensor product
representations, we construct homomorphisms for these data structures into
geometric vector spaces. We prove that the structure-building functions as well
as simple processors for minimalist languages can be realized by piecewise
linear operators in representation space. We also propose harmony, i.e. the
distance of an intermediate processing step from the final well-formed state in
representation space, as a measure of processing complexity. Finally, we
illustrate our findings by means of two particular arithmetic and fractal
representations.Comment: 43 pages, 4 figure
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