Rules and meta-rules in the framework of possibility theory and possibilistic logic

Abstract

Abstract:The contribution of Lotfi Zadeh to the development of fuzzy logic, goes far beyond the introduction of the seminal concept of a fuzzy set and has multiple facets. This article, as a small tribute to the corpus of ideas, notions and results brought together over almost five decades by Zadeh, singles out and illustrates two of his most stimulating, thoughtprovoking and fruitful creations: fuzzy rules on the one hand, and possibility theory on the other hand. Indeed, the modeling of conditional statements of the form "if x is A then y is B" plays a crucial role in any attempt at formalizing human reasoning. Starting from the expression of different forms of fuzzy rules that have been identified in the setting of possibility theory, we study their counterparts in the extensions of possibilistic logic. A distinction between rules and meta-rules is especially emphasized, in the representational setting of possibility theory. It amounts to viewing rules as pieces of knowledge that contribute to the partial specification of a unique epistemic state, while meta-rules characterize constraints between specified epistemic states, as in possibilistic answer set programming.

Weak and Strong Disjunction in Possibilistic ASP

“…As necessity measures do not have the max-decomposability property, we have a choice of how to interpret the disjunction in the head. This is similar to the choice one has for the semantics of disjunction when characterizing ASP using autoepistemic logic [12] or using meta-rules in possibilistic logic [9]. A possibilistic disjunctive rule p = (r, λ) with r = a 0 ; ...; a k ← a k+1 , ..., a m , not a m+1 , ..., not a n can either be interpreted as the constraint…”

University–industry collaboration: using meta-rules to overcome barriers to knowledge transfer

“…In this way they may be compared to grammatical syntax which dictates the order of sentence components rather than sentence content (Dubois et al 2011).…”

“…In this way the facilitation of knowledge flows can enable the codification of tacit (Alexander and Childe 2011) knowledge through feedforward and feedback mechanisms (Vargas et al 2016) which aids organisational learning through creating a platform for project-level co-operation and knowledge acquisition (Liao et al 2017). An important consideration here is the 'epistemic' and syntactical nature of meta-rules which highlight the order of organisational policy application (Dubois et al 2011;Davis 1980). Consequently, the meta-rule framework can aid knowledge distribution from the corporate, through to the departmental and project levels and thus enhance organisational learning through multi-level knowledge flows.…”

“…Meta-rules are defined as 'rules about rules' and 'information about information' (Davis 1980), applying to the 'epistemic' rather than the 'object' level. They can help clarify the order of application of existing, codified rules within organisations (Dubois et al 2011) to help organisational decision making. It is proposed that these properties can help resolve tensions arising from conflicting priorities between academics, knowledge transfer offices and industry and help resolve, inconsistent application of policies within and between organisations.…”

Possibility Theory and Its Applications: Where Do We Stand?

“…This extension, still under study [78], puts together the KD modal logic and basic possibilistic logic. Recently it has been shown that nonmonotonic logic programing languages can be translated into generalized possibilistic logic, making the meaning of negation by default in rule much more transparent [85]. This move from basic to generalized possibilistic logic also enables further extensions to the multi-agent and the multi-source case [76] to be considered.…”