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The general theme of this article is the actual practice of how definitions are justified and formulated in mathematics. The theoretical insights of this article are based on a case study of topological definitions of chaos. After introducing this case study, I identify the three kinds of justification which are important for topological definitions of chaos: natural-world-justification, condit...

This paper gives an explication of our intuitive notion of strength of justification in a controversial debate. It defines a thesis’ degree of justification within the bipolar argumentation framework of the theory of dialectical structures as the ratio of coherently adoptable positions according to which that thesis is true over all coherently adoptable positions. Broadening this definition, th...

This paper presents a characterisation of and definitions for the phenomenon of masking in the context of justifications for entailments in ontologies. In essence masking is present within a justification, over a set of justifications, or over a complete ontology when the number of justifications for an entailment does not reflect the number of reasons for that entailment. Four types of masking...

This paper exhibits some problematic cases of defeasible or nonmonotonic reasoning that tend to be handled incorrectly by all of the theories of defeasible and nonmonotonic reasoning in the current literature. The paper focuses particularly on default logic, circumscription, and the author’s own argument-based approach to defeasible reasoning. A proposal is made for how to deal with these probl...

Justification Logic is a family of epistemic logical systems obtained from modal logics of knowledge by adding a new type of formula t:F , which is read t is a justification for F . The principal epistemic modal logic S4 includes Tarski’s well-known topological interpretation, according to which the modality 2X is read the Interior of X in a topological space (the topological equivalent of the ...

Justification logics are refinements of modal logics, where justification terms replace modalities. Modal and justification logics are connected via the so-called realization theorems. We develop a general constructive method of proving the realization of a modal logic in an appropriate justification logic by means of cut-free modal nested sequent systems. We prove a constructive realization th...

According to a standard view of the second law of thermodynamics, our belief in the second law can be justified by pointing out that low entropy macrostates are less probable than high entropy macrostates, and then noting that a system in an improbable state will tend to evolve toward a more probable state. I would like to argue that this justification of the second law of thermodynamics is fun...

Committees of classifiers with learning capabilities have good performance in a variety of domains. We focus on committees of agents with learning capabilities where no agent is omniscient but has a local, limited, individual view of data. In this framework, a major issue is how to integrate the individual results in an overall result—usually a voting mechanism is used. We propose a setting whe...