On the Entailment Problem for a Logic of Typicality

Authors: Richard Booth, Giovanni Casini, Thomas Andreas Meyer, Ivan José Varzinczak

IJCAI 2015 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Theoretical We study the different forms of entailment in an abstract formal setting, obtained by proposing a set of postulates that, at first glance, seem appropriate for any notion of entailment with regard to typicality. Our first important result is a negative one, though. It is an impossibility result proving that the set of postulates cannot all be satisfied simultaneously.
Researcher Affiliation Academia Richard Booth Mahasarakham University Thailand ribooth@gmail.com; Giovanni Casini CAIR, Univ. of Pretoria and CSIR Meraka South Africa; Univ. of Luxembourg Luxembourg giovanni.casini@gmail.com; Thomas Meyer CAIR, Univ. of Cape Town and CSIR Meraka South Africa tmeyer@cs.uct.ac.za; Ivan Varzinczak Universidade Federal do Rio de Janeiro Brazil ijv@ufrj.br
Pseudocode Yes We construct a sequence p R0, R1, . . .q of ranked interpretations as follows, where Ri x U, ăiy (i.e., the set of valuations V is always the full set of all valuations): Step 1 Initialise ă0: H (start with an initial ranked interpretation in which all valuations are equally preferred.) Step 2 Si 1 : JKKRi (separate the valuations which satisfy K w.r.t. the current ranked interpretation Ri from those that do not.) Step 3 If Si 1 Si then STOP and return R p Kq Ri Ó Si 1 (if the division is the same as in the previous round then eliminate completely from the current ranked interpretation those valuations that do not satisfy K w.r.t. Ri and return the interpretation that remains.) Step 4 Otherwise ăi 1: ăi Yp Si 1 ˆ Sc i 1q, i : i 1 and go to Step 2 (otherwise create a new ranked interpretation Ri 1 by making every valuation not in Si 1 less plausible than every valuation in Si 1. Note that Sc here denotes Uz S.)
Open Source Code No The paper does not provide any explicit statement or link indicating the availability of open-source code for the described methodology.
Open Datasets No This paper is theoretical research focusing on logical entailment and does not involve experimental training with datasets.
Dataset Splits No This paper is theoretical research and does not involve experimental validation with datasets or splits.
Hardware Specification No This paper is theoretical research and does not describe any experimental setup that would require hardware specifications.
Software Dependencies No This paper is theoretical research and does not describe any experimental setup that would require specific software dependencies with version numbers.
Experiment Setup No This paper is theoretical research and does not describe an experimental setup with hyperparameters or system-level training settings.