On the Decidability and Complexity of Integrating Ontologies and Rules

2005 ◽  
Author(s):  
Riccardo Rosati
Keyword(s):  
Decidability And Complexity

scholarly journals Mīmāṃsā deontic reasoning using specificity: a proof theoretic approach

2020 ◽  
Author(s):  
Björn Lellmann ◽  
Francesca Gulisano ◽  
Agata Ciabattoni
Keyword(s):  
Deontic Logic ◽  
Sequent Calculus ◽  
Prima Facie ◽  
Theoretic Approach ◽  
Deontic Reasoning ◽  
Complexity Results ◽  
Restricted Form ◽  
Philosophical School ◽  
Decidability And Complexity ◽  
Potential Use

Abstract Over the course of more than two millennia the philosophical school of Mīmāṃsā has thoroughly analyzed normative statements. In this paper we approach a formalization of the deontic system which is applied but never explicitly discussed in Mīmāṃsā to resolve conflicts between deontic statements by giving preference to the more specific ones. We first extend with prohibitions and recommendations the non-normal deontic logic extracted in Ciabattoni et al. (in: TABLEAUX 2015, volume 9323 of LNCS, Springer, 2015) from Mīmāṃsā texts, obtaining a multimodal dyadic version of the deontic logic $$\mathsf {MD}$$ MD . Sequent calculus is then used to close a set of prima-facie injunctions under a restricted form of monotonicity, using specificity to avoid conflicts. We establish decidability and complexity results, and investigate the potential use of the resulting system for Mīmāṃsā philosophy and, more generally, for the formal interpretation of normative statements.

scholarly journals DECIDABILITY AND COMPLEXITY IN AUTOMATIC MONOIDS

2005 ◽  
Vol 16 (04) ◽  
pp. 707-722 ◽  
Author(s):  
MARKUS LOHREY
Keyword(s):  
Cayley Graph ◽  
Word Problem ◽  
Hyperbolic Group ◽  
Order Theory ◽  
First Order ◽  
First Order Theory ◽  
Decidability And Complexity

Several complexity and decidability results for automatic monoids are shown: (i) there exists an automatic monoid with a P-complete word problem, (ii) there exists an automatic monoid such that the first-order theory of the corresponding Cayley-graph is not elementary decidable, and (iii) there exists an automatic monoid such that reachability in the corresponding Cayley-graph is undecidable. Moreover, it is shown that for every hyperbolic group the word problem belongs to LOGCFL, which improves a result of Cai [8].

DEL-based epistemic planning: Decidability and complexity

2020 ◽  
Vol 287 ◽  
pp. 103304 ◽  
Author(s):  
Thomas Bolander ◽  
Tristan Charrier ◽  
Sophie Pinchinat ◽  
François Schwarzentruber
Keyword(s):  
Decidability And Complexity
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