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. |