- Introduction
- TS implementation: Semantic Calculator
- Non-canonical Coordination in the Transformational Approach
- Transformational Semantics (TS) on a Tree Bank

- 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 inverse linking.

**References**- Transformational Semantics is the outcome of the
conceptual simplification of
Applicative Abstract Categorial
Grammars
AACG1.pdf [263K]

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.NewLandscapes-talk.pdf [176K]

Gradually Transforming Syntax to Semantics

Talk at the workshop ``New Landscapes in Theoretical Computational Linguistics''. Ohio State University, October 16, 2016.

- 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 entailments.
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.

**Version**- The current version is February 2018
**References**- 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.Syntax.hs [<1K]

Term language for the surface syntaxSem.hs [4K]

Syntax-semantics interface: the correspondence between the abstract form (with raised quantifiers) and logic formulasLogic.hs [17K]

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 proversQuan.hs [15K]

Extending the abstract language with in-situ and raised quantifiers, and defining quantifier raisingPronoun.hs [5K]

Extending the abstract language with pronouns and the transformations for anaphora resolutionExtensible Effects are used in this project

- 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 generalized quantifiers.
**Version**- The current version is March 2017
**References**- 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_3Coord.hs [17K]

Coordination reduction transformations programmed in TS. The code includes all examples from the paper.

- 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.

**Version**- The current version is January 2018
**References**- Fracas.pdf [180K]

Transformational Semantics on a Tree Bank

New Frontiers in Artificial Intelligence. JSAI-isAI 2017. Lecture Notes in Computer Science, vol 10838, pp. 241-252. Springer.

doi:10.1007/978-3-319-93794-6_17Fracas-talk.pdf [156K]

Talk at LENLS 2017, Tokyo, Japan, November 14, 2017PPL-poster.pdf [66K]

Poster presented at the Programming and Programming Languages Workshop (PPL2018), Yonago, Japan, March 6, 2018.TreebankRun.hs [29K]

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 proverTreebank.hs [23K]

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.psd [89K]

FraCAS corpus (Part 1: quantifiers) annotated according to the Penn Historical Corpora system, very kindly provided by Alastair ButlerSExpParser.hs [4K]

The parser for the annotated tree bank