Towards Logics that Model Natural Reasoning

Summary

Logic has its roots in the study of valid argument, but while traditional logicians worked with natural language directly, modern approaches first translate natural arguments into an artificial language. The reason for this step is that some artificial languages now have very well developed inferential systems. There is no doubt that this is a great advantage in general, but for the study of natural reasoning it is a drawback that the original linguistic forms get lost in translation. The program proposed here is aimed at developing a general theory of the natural logic behind human reasoning and human information processing by studying formal logics that operate directly on linguistic representations. Translation of natural language into one of the usual logical languages is in fact unnecessary, we submit, because one level of linguistic representation, that of Logical Form, can meaningfully be identified with the language of an existing and well-understood logic, a restricted form of the theory of types. It is not difficult to devise inference systems for this language, and it is thus possible to study---with the help of all the instruments of modern logic---reasoning systems that are based directly on linguistic representations.

We define three subprojects. One will investigate linguistic consequences of this insight and will result in a proof theoretical form of natural language semantics. Another will study the computational logic of different modes of natural reasoning, each based on the systematic search for models that is often taken to be the motor of human inference. A third project will compare the theoretical complexity of model checking tasks for natural language with the cognitive difficulty of these tasks as experienced by human subjects.

Output

Thesis

  • L Abzianidze(2016): A Natural Proof System for Natural Language , Ridderkerk  January 20, 2017
  • J Reinert(2017): Impossible Intentionality , Tilburg  December 5, 2017

Chapter in book

  • J. Alama, H. Jales Ribeiro, S. Uckelman(2012): Inside Arguments: Logic and the Study of Argumentation pp. 207 - 222 , Newcastle
  • S. Uckelman(2012): Saint Anselm of Canterbury and His Legacy pp. 405 - 426 , Toronto
  • M. Aloni, R.A. Muskens, V. Kimmelman, F. Roelofsen, G. Sassoon, K. Schulz, M. Westera(2012): Logic, Language and Meaning pp. 441 - 449 , Berlin Heidelberg
  • T Murata, D Bekki, K Mineshima, L Abzianidze(2015): New Frontiers in Artificial Intelligence pp. 66 - 82

Scientific article

  • S. Uckelman(2011): Deceit and indefeasible knowledge: the case of dubitatio Journal of Applied Non-Classical Logics pp. 503 - 519
  • S. Uckelman(2012): Arthur Prior and medieval logic Synthese pp. 349 - 366
  • S. Uckelman(2012): Interactive logic in the Middle Ages Logic and Logical Philosophy pp. 439 - 471
  • S. Uckelman(2012): Medieval Disputationes de obligationibus as formal dialogue systems Argumentation pp. 000 - 000
  • S. Uckelman(2012): Prior on an insolubilium of Jean Buridan Synthese pp. 487 - 498
  • J Reinert(2013): Ontological omniscience in Lewisian modal realism Analysis pp. 676 - 682
  • R A Muskens, S Wintein(2014): From Bi-facial Truth to Bi-facial Proofs Studia Logica pp. 545 - 558
  • S Wintein, R A Muskens(2015): Analytic Tableaux for all of SIXTEEN_3 Journal of Philosophical Logic pp. 473 - 487
  • R A Muskens, S Wintein(2015): A Gentzen Calculus for Nothing but the Truth Journal of Philosophical Logic pp. 1 - 15

Details

Project number

360-80-050

Main applicant

Dr. R.A. Muskens

Affiliated with

Tilburg University, Faculteit Geesteswetenschappen

Team members

Dr. L.A. Abzianidze, Dr. R.A. Muskens, Drs. J. Reinert, Dr. B.M. Tomaszewicz, Dr. S.L. Uckelman, Dr. S.A. Uckelman

Duration

01/09/2011 to 31/12/2015