Transformational Semantics (TS): Gradually Transforming Syntax to Semantics
Transformational Semantics (TS) formalizes,
restraints and makes rigorous the transformational approach epitomized
by QR and Transformational Grammars: deriving the meaning
(a logical formula) by a series of
transformations from a suitably abstract (tecto-) form of a sentence.
TS generalizes various `monad' or `continuation-based'
computational approaches, abstracting away irrelevant details (such as
monads) while overcoming their rigidity and brittleness. Unlike
QR, each transformation in TS is rigorously and precisely
defined, typed, and deterministic. The restraints of TS and the
sparsity of the choice points (in the order of applying the
deterministic transformation steps) make it easier to derive negative
predictions and control over-generation.
Initially, TS has been applied to the analyses of quantifier ambiguity, scoping
islands and binding, crossover, topicalization, and
- Transformational Semantics is the outcome of the conceptual simplification of Applicative Abstract Categorial Grammars
Applicative Abstract Categorial Grammars in Full Swing
New Frontiers in Artificial Intelligence: JSAI-isAI 2015 Workshops, Kanagawa, Japan, November 16-18, 2015, Revised Selected Papers
Lecture Notes in Artificial Intelligence, v10091, pp. 66--78, 2017 doi:10.1007/978-3-319-50953-2_6
Although the paper refers to Applicative Abstract Categorial Grammars in the title, it is actually about TS. It is the first paper on TS.
Gradually Transforming Syntax to Semantics
Talk at the workshop ``New Landscapes in Theoretical Computational Linguistics'', Ohio State University, October 16, 2016.
TS implementation: Semantic Calculator
Because TS is precisely specified, its transformations can be carried
out mechanically, by a computer. The current implementation takes the
form of a domain-specific language embedded in Haskell. It was
originally intended as a semantic theory design aid: to interactively
try various transformations, observe their results or failures. It can
also be used in `batch mode', to fully
automatically derive the meanings of tree bank sentences and their
As befits its origins in Abstract Categorial Grammars, TS is implemented
in the tagless-final style.
TS transformations are typically presented in papers as extended
top-down tree transducers: that is, tree-rewriting rules that attempt
to pattern-match on tree branches starting from the root. The rules'
patterns are deep: they can match nodes appearing deeply inside the
current branch. This context-sensitive matching and re-writing is
actually implemented bottom-up, building the transformed tree up from
the leaves of the original one.
Writing out the TS-transformed abstract-form term as the set-theoretic
logical formula relies on extensible-effects. One obvious effect is
generating fresh identifiers; the other is accumulating
auxiliary formulas. The two effects together implement
what may be called
`let-insertion': giving a name to the relation defined by a
logical formula -- in effect realizing set-comprehension.
- The current version is February 2018.
- Abstract.hs [11K]
Definition of the abstract form -- a tecto-grammatical
form of a sentence. The file also defines the transformation
from the abstract form to surface syntax. The abstract form is later
extended with quantifiers, pronouns and various coordinators.
Term language for the surface syntax
Syntax-semantics interface: the correspondence between the abstract form (with raised quantifiers) and logic formulas
The language of meaning: First-order predicate logic. The logic formulas can be written out in the TPTP format, commonly used by first-order theorem provers
Extending the abstract language with in-situ and raised quantifiers, and defining quantifier raising
Extending the abstract language with pronouns and the transformations for anaphora resolution
Non-canonical Coordination in the Transformational Approach
We apply TS to right-node raising (RNR), gapping and other instances
of non-constituent coordination. Our analyses straightforwardly
represent the intuition that coordinated phrases must in some sense be
`parallel', with a matching structure. Coordinated material is not
necessarily constituent -- even `below the surface' -- and we do not
pretend it is. We answer the Kubota, Levine and Moot challenge (the
KLM problem) of analyzing
RNR and gapping without directional types, yet avoiding
massive over-generation. We thus formalize the old idea of
`coordination reduction' and show how to make it work for
- The current version is March 2017.
- Coord.pdf [241K]
Non-canonical Coordination in the Transformational Approach
New Frontiers in Artificial Intelligence: JSAI-isAI 2016 Workshops, Kanagawa, Japan, November 14-16, 2016, Revised Selected Papers
Lecture Notes in Computer Science, v10247, pp. 33--44, 2017 doi:10.1007/978-3-319-61572-1_3
Coordination reduction transformations programmed in TS. The code includes all examples from the paper.
Transformational Semantics (TS) on a Tree Bank
The rigorous nature of TS makes it easier to carry out analyses
mechanically, by a computer. We report on such a mechanical, fully
automatic application of TS to a tree bank of FraCAS text entailment
problems (generalized quantifier section). Set-theoretic logical
formulas derived by TS as meanings for input sentences are submitted
to an automatic first-order theorem prover to decide entailment. A
characteristic feature of our approach is the exhaustive enumeration
of quantifier and other such ambiguities.
Overall TS proved just as capable as natural logic in inferences
involving a variety of generalized quantifiers. Still open is the
problem of mechanically dealing with bare plurals.
- The current version is January 2018.
- Fracas-talk.pdf [156K]
Talk at LENLS 2017, Tokyo, Japan, November 14, 2017
The main function of the FraCaS application: select a FraCAS problem,
transform its sentences into logical formulas,
which are then submitted to the E theorem prover
This code reads treebank-annotated parse trees and
converts them to the Haskell code that spells out the abstract form.
To be precise, it creates Template Haskell terms, to be type-checked and
transformed in TreebankRun.hs
FraCAS corpus (Part 1: quantifiers) annotated according to the Penn Historical Corpora system, very kindly provided by Alastair Butler
The parser for the annotated tree bank
Last updated February 5, 2018
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