Justification Logic and Applications

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Artemov, Fitting, and Nogina will continue their development of Justification Logic, which offers a possible breakthrough in the quest to create a fundamental theory of knowledge, belief, and evidence, and has the potential for significant impact on applications. The celebrated account of knowledge as "justified true belief," which is attributed to Plato, has long been a focus of epistemic studies. About a half-century ago, the notions of knowledge and belief acquired formalization by means of modal logic. However the notion of justification, an essential element of epistemic studies, was conspicuously absent, and this led to well-known deficiencies inherent in modal logics of knowledge.Justification Logic extends the logic of knowledge in three major ways. First, it adds a long-anticipated mathematical notion of justification, making the logic more expressive. We now have the capacity to reason about justifications, simple and compound. We can compare different pieces of evidence pertaining to the same fact. We can measure the complexity of justifications, thus connecting the logic of knowledge to a rich complexity theory, etc. Second, justification logic furnishes a new, evidence-based foundation for the logic of knowledge, according to which `F is known' is interpreted as `F has an adequate justification.' Third, justification logic provides a novel, evidence-based mechanism of truth tracking which can be a valuable tool for extracting robust justifications from a larger body of justifications which are not necessarily reliable.Knowledge, belief, and evidence are fundamental concepts whose significance spans many areas of human activity: computer science and artificial intelligence, mathematics, economics and game theory, cryptography, philosophy, and other disciplines. Justification Logic promises significant impact on the aforementioned areas. In particular, the capacity to keep track of pieces of evidence, compare them, and select those that are appropriate would be a valuable new tool.