Logic Journal of the IGPL 17 (4):375–394 (2009)

Joanna Golinska-Pilarek
University of Warsaw
We present a relational proof system in the style of dual tableaux for a multimodal propositional logic for order of magnitude qualitative reasoning to deal with relations of negligibility, non-closeness, and distance. This logic enables us to introduce the operation of qualitative sum for some classes of numbers. A relational formalization of the modal logic in question is introduced in this paper, i.e., we show how to construct a relational logic associated with the logic for order-of-magnitude reasoning and its dual tableau system which is a validity checker for the modal logic. For that purpose, we define a validity preserving translation of the modal language into relational language. Then we prove that the system is sound and complete with respect to the relational logic defined as well as with respect to the logic for order of magnitude reasoning. Finally, we show that in fact relational dual tableau does more. It can be used for performing the four major reasoning tasks: verification of validity, proving entailment of a formula from a finite set of formulas, model checking, and verification of satisfaction of a formula in a finite model by a given object
Keywords relational logic  qualitative reasoning  dual tableaux  Rasiowa-Sikorski proof system
Categories (categorize this paper)
DOI 10.1093/jigpal/jzp016
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 65,593
Through your library

References found in this work BETA

Causal Approximations.P. Pandurang Nayak - 1994 - Artificial Intelligence 70 (1-2):277-334.
Order of Magnitude Reasoning.Olivier Raiman - 1991 - Artificial Intelligence 51 (1-3):11-38.

Add more references

Citations of this work BETA

A Multimodal Logic for Closeness.M. Ojeda-Aciego, E. Muñoz-Velasco & A. Burrieza - 2017 - Journal of Applied Non-Classical Logics 27 (3-4):225-237.

Add more citations

Similar books and articles

Reasoning with Qualitative Velocity: Towards a Hybrid Approach.Joanna Golinska-Pilarek & Emilio Munoz Velasco - 2012 - In Emilio Corchado, Vaclav Snasel, Ajith Abraham, Michał Woźniak, Manuel Grana & Sung-Bae Cho (eds.), Hybrid Artificial Intelligent Systems. Springer. pp. 635--646.
Relational Proof Systems for Spatial Reasoning.Joanna Golińska-Pilarek & Ewa Orlowska - 2006 - Journal of Applied Non-Classical Logics 16 (3-4):409-431.
Relational Dual Tableaux for Interval Temporal Logics.David Bresolin, Joanna Golinska-Pilarek & Ewa Orlowska - 2006 - Journal of Applied Non-Classical Logics 16 (3-4):251–277.
Implementing a Relational Theorem Prover for Modal Logic K.Angel Mora, Emilio Munoz Velasco & Joanna Golińska-Pilarek - 2011 - International Journal of Computer Mathematics 88 (9):1869-1884.
A Proof System for Contact Relation Algebras.Ivo Düntsch & Ewa Orłowska - 2000 - Journal of Philosophical Logic 29 (3):241-262.
Rasiowa-Sikorski Proof System for the Non-Fregean Sentential Logic SCI.Joanna Golinska-Pilarek - 2007 - Journal of Applied Non-Classical Logics 17 (4):509–517.


Added to PP index

Total views
13 ( #753,147 of 2,462,051 )

Recent downloads (6 months)
1 ( #448,768 of 2,462,051 )

How can I increase my downloads?


My notes