Possibilistic Logic: From Certainty-Qualified Statements to Two-Tiered Logics – A Prospective Survey

Abstract

Open Archive Toulouse Archive OuverteOATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible To cite this version: Dubois, Didier and Prade, Henri

Provenance Calculus and Possibilistic Logic: A Parallel and a Discussion

“…The complexity remains similar to the one of classical logic (it is multiplied by the logarithm of the number of distinct certainty levels present in the PL base we start with). Introductions, details, applications to various artificial intelligence problems can be found in [32,28,33,34].…”

Possibility Theory and Possibilistic Logic: Tools for Reasoning Under and About Incomplete Information

“…Possibilistic logic (PL) [31,39,41,42] amounts to a classical logic handling of certaintyqualified statements. Certainty is estimated in the setting of possibility theory as a lower bound of a necessity set-function.…”

“…The basic formulas are pairs (x, y) and stand for "y is a reason for believing x". Another perspective is reasoning about other agents' beliefs as in the muddy children problem [42].…”

Logic-Sensitivity of Aristotelian Diagrams in Non-Normal Modal Logics

“…Aristotelian diagrams, such as the so-called square of opposition, visualize a number of formulas from some logical system, as well as certain logical relations holding between them. These diagrams have a rich history in philosophy and logic [1][2][3], and today they are also widely used in artificial intelligence, to study and compare knowledge representation formalisms such as the rough set theory [4][5][6], formal concept analysis and possibility theory [7][8][9], formal argumentation theory [10][11][12][13], fuzzy set theory [14][15][16][17], logical theories of analogical and proportional reasoning [18][19][20][21][22][23], probabilistic logic [24][25][26] and multiple-criterion decision-making [27][28][29]. Without a doubt, the oldest and most widely used Aristotelian diagram is the square of opposition for the categorical statements from syllogistics, such as 'all Greeks are mortal' and 'some Greeks are mortal'.…”