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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 inverse linking.

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.


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 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.

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.

Syntax.hs [<1K]
Term language for the surface syntax

Sem.hs [4K]
Syntax-semantics interface: the correspondence between the abstract form (with raised quantifiers) and logic formulas

Logic.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 provers

Quan.hs [15K]
Extending the abstract language with in-situ and raised quantifiers, and defining quantifier raising

Pronoun.hs [5K]
Extending the abstract language with pronouns and the transformations for anaphora resolution

Extensible Effects


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 generalized quantifiers.
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

Coord.hs [17K]
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

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 prover

Treebank.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 Butler

SExpParser.hs [4K]
The parser for the annotated tree bank

Last updated February 5, 2018

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