Reasoning consistently about inconsistency

Patching et al. and Hinde et al. in their work on truth-space mass assignments, presented a semantic unification function and a semantic separation function for mass assignment logic that dealt with inconsistency. This paper takes these two functions and while preserving the outside inconsistencies shows how inconsistency can be reasoned about in a consistent manner. This means that inconsistency that arises outside the system need not enter the system, but needs to be represented within the system, and can therefore be extracted appropriately as output from the system to emerge as inconsistency on the outside. The internal reasoning system need therefore only concern itself with belief in truth, falsity and uncertainty

Reasoning Consistently about Inconsistency

Patching et al. and Hinde et al. in their work on truth-space mass assignments, presented a semantic unification function and a semantic separation function for mass assignment logic that dealt with inconsistency. This paper takes these two functions and while preserving the outside inconsistencies shows how inconsistency can be reasoned about in a consistent manner. This means that inconsistency that arises outside the system need not enter the system, but needs to be represented within the system, and can therefore be extracted appropriately as output from the system to emerge as inconsistency on the outside. The internal reasoning system need therefore only concern itself with belief in truth, falsity and uncertainty

On a Partial Decision Method for Dynamic Proofs

This paper concerns a goal directed proof procedure for the propositional fragment of the adaptive logic ACLuN1. At the propositional level, it forms an algorithm for final derivability. If extended to the predicative level, it provides a criterion for final derivability. This is essential in view of the absence of a positive test. The procedure may be generalized to all flat adaptive logics.Comment: 18 pages. Originally published in proc. PCL 2002, a FLoC workshop; eds. Hendrik Decker, Dina Goldin, Jorgen Villadsen, Toshiharu Waragai (http://floc02.diku.dk/PCL/

Quantum Non-Objectivity from Performativity of Quantum Phenomena

We analyze the logical foundations of quantum mechanics (QM) by stressing non-objectivity of quantum observables which is a consequence of the absence of logical atoms in QM. We argue that the matter of quantum non-objectivity is that, on the one hand, the formalism of QM constructed as a mathematical theory is self-consistent, but, on the other hand, quantum phenomena as results of experimenter's performances are not self-consistent. This self-inconsistency is an effect of that the language of QM differs much from the language of human performances. The first is the language of a mathematical theory which uses some Aristotelian and Russellian assumptions (e.g., the assumption that there are logical atoms). The second language consists of performative propositions which are self-inconsistent only from the viewpoint of conventional mathematical theory, but they satisfy another logic which is non-Aristotelian. Hence, the representation of quantum reality in linguistic terms may be different: from a mathematical theory to a logic of performative propositions. To solve quantum self-inconsistency, we apply the formalism of non-classical self-referent logics

An Approach to Cope with Ontology Changes for Ontology-based Applications

Keeping track of ontology changes is becoming a critical issue for ontology-based applications because updating an ontology that is in use may result in inconsistencies between the ontology and the knowledge base, dependent ontologies and dependent applications/services. Current research concentrates on the creation of ontologies and how to manage ontology changes in terms of the attempts to ease the communications between ontology versions and keep consistent with the instances, and there is little work available on controlling the impact to dependent applications/services which is the aims of the system presented in this paper. The approach we propose in this paper is to manually capture and log ontology changes, use this log to analyse incoming RDQL queries and amend them as necessary. Revised queries can then be used to query the knowledge base of the applications/services. We present the infrastructure of our approach based on the problems and scenarios identified within ontology-based systems. We discuss the issues met during our design and implementation, and consider some problems whose solutions will be beneficial to the development of our approach