Deductive Systems with Multiple-Conclusion Rules and the Disjunction Property

Citkin, Alex

doi:10.3390/axioms8030100

Cited by 2 publications

(2 citation statements)

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“…The most common definition comprises deductive systems as: "A set of rules R and axioms. Since axioms can be viewed as rules without premises, we assume that a deductive system is a set of rules and a procedure for derivation such that Γ L A if and only if A can be derived from Γ by rules R" [3].…”

Section: Introductionmentioning

confidence: 99%

The Formal Framework for Collective Systems

Palak

Wojtkiewicz

2021

Axioms

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Automated reasoning is becoming crucial for information systems. Building one uniform decision support system has become too complicated. The natural approach is to divide the task and combine the results from different subsystems into one uniform answer. It is the basic idea behind the system approach, where one solution is a composition of multiple subsystems. In this paper, the main emphasis is on establishing the theoretical framework that combines various reasoning methods into a collective system. The system’s formal abstraction uses graph theory and provides a discussion on possible aggregation function definitions. The proposed framework is a tool for building and testing specific approaches rather than the solution itself.

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Section: Introductionmentioning

confidence: 99%

The Formal Framework for Collective Systems

Palak

Wojtkiewicz

2021

Axioms

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“…In [8], A. Citkin studies the deductive systems with multiple conclusion rules which admit the introduction of meta-disjunction. Using the defined notion of the inference with multiple-conclusion rules, it is shown that in the logics enjoying the disjunction property, any derivable rule can be inferred from the single-conclusion rules and a single multiple-conclusion rule, which represents the disjunction property.…”

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confidence: 99%