The Logical Linguistic Legacy of Montague Grammar

Dear Colleagues,

“… But when ye come,

and all the flowers are dying,

If I am dead, as dead I well may be.

Ye'll come and find the place where I am lying,

And kneel and say an Ave there for me.”

Danny Boy,

Frederic Weatherly (1848-1929)

This Special Issue is dedicated, with gratitude and appreciation, to Richard Montague and Joachim Lambek for the elegance and beauty of their contributions to logical linguistics.

Notwithstanding the incredible achievements of statistical linguistics, in a succession of probabilistic dependencies confidence tends to 0%, whereas in a succession of logical dependencies confidence is always 100% end-to-end; this is needed in life-critical cases such as nuclear, chemical, or biological threat, security, medicine, finances, avionics, …: in fact … in fact in potentially anything.

In the context of the hegemony of statistical linguistics, the current Special Issue sends out a call for a renaissance of logical linguistics.

Richard Montague (1930-1971) was a philosopher at the University of Berkley, California, in the 1960s, who believed that it was immoral to be paid to philosophise. He amassed great wealth in real estate and met with his students while driving his expensive car about town. He died at home asphyxiated after picking up unknowns in a bar.

Richard Montague's work in logical linguistics defined a framework for compositional semantics (Montague 1970a), gave logical semantics to a significant fragment of English (Montague 1970b), and included, in particular, a treatment of quantification (Montague 1973) that had come to him while teaching natural deduction; all of this occurred at a time when the formalisation of the semantics of natural language was generally considered to be impossible.

In the preface to Chomsky (1957), Noam Chomsky makes a perfect plea for formal linguistics, but he has reneged on formal methods with disparaging remarks to the effect of “premature” or “formalisation for formalisation’s sake”.

Although Montague’s syntax was rigorous, he considered syntax to be important only as a means to semantics, and he did not trouble to formalise it.  However, in the 1950s, another mathematical linguist, Joachim Lambek (1922-2014), had proportioned the foundation of logical syntax (categorial grammar, Lambek 1958).

Lambek’s logical syntax serves to formalise the syntactic side of Montague grammar. The resulting marriage of logical syntax and logical semantics (Moortgat 1988; Morrill 1994; …) is the logical linguistic legacy of Richard Montague and Joachim Lambek.

We invite potential contributors to submit articles of up to 25 pages, including references, to this Special Issue of Philosophies, on any aspects of this logical and linguistic legacy. Contributors are requested to keep in mind that this journal integrates diverse forms of inquiry and reaches a broad audience. This includes experts on the subject matter experts and readers who are interested in the topic but may not have specialised knowledge.

In particular, an introduction to each paper should be included to present philosophical questions and problems, the solutions to which constitute the objectives of the work. Given the technical nature of the field, all potential contributors will be supplied with a text “A formal synopsis of Lambek-Montague grammar” to appear as a foreword to the Special Issue and provide a source and reference for more standard definitions, formalism, and technicalities.

Additional technicalities/formalities should be “user-friendly”, and we encourage contributors to minimise the use of additional technical terminology or undefined concepts by referring, where possible, to the context provided by this synopsis; if an explanation within the text is impractical, appropriate references to relevant literature should be provided.

References

Chomsky, N. (1957) Syntactic Structures, Mouton, The Hague.

Lambek, J. (1958) `The mathematics of sentence structure’, American Mathematical Monthly, 65, 3, 154-170.

Montague, R. (1970a) `Universal grammar’, Theory, 36, 3, 373-398.

Montague, R. (1970b) `English as a formal language’ in B. Visentini et al. (eds.) Linguaggi nella Società e nella Tecnica, Edizioni de Communita, Milan, 189-224.

Montague, R. (1973) `The proper treatment of quantification in ordinary English’, in K.J.J. Hintikka et al. (eds.) Approaches to Natural Language, Synthese Library 49, Reidel, Dordrecht, 221-242.

Moortgat, M. (1988) Categorial Investigations: Logical and Linguistic Aspects of the Lambek Calculus, Foris, Dordrecht.

Morrill, G. (1994) Type Logical Grammar: Categorial Logic of Signs, Kluwer Academic Press, Dordrecht.

Dr. Glyn Morrill
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a double-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Philosophies is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

• compositionality
• focusing
• formulas-as-types/proofs-as-programs Curry–Howard correspondence
• intensional logic
• lambda calculus
• logical categorial grammar
• logical syntax and semantics
• parsing-as-deduction
• proof nets
• type logic