A Type-Theoretic Framework for Formal Reasoning with Different Logical Foundations
نویسنده
چکیده
A type-theoretic framework for formal reasoning with different logical foundations is introduced and studied. With logic-enriched type theories formulated in a logical framework, it allows various logical systems such as classical logic as well as intuitionistic logic to be used effectively alongside inductive data types and type universes. This provides an adequate basis for wider applications of type theory based theorem proving technology. Two notions of set are introduced in the framework and used in two case studies of classical reasoning: a predicative one in the formalisation of Weyl’s predicative mathematics and an impredicative one in the verification of security protocols.
منابع مشابه
Game-Theoretic Foundations for Argumentation
Game theory is becoming central to the design and analysis of computational mechanisms in which multiple entities interact strategically. In particular, the tools of mechanism design are used extensively to engineer incentives for truth-revelation into resource-allocation and preferenceaggregation protocols, as evident in the work on combinatorial auctions and voting. On the other hand, traditi...
متن کاملLogical Case Memory Systems: Foundations and Learning Issues Forschungsbericht Autor(en) / Author(s)
The focus of this paper is on the introduction of a quite general type of case-based reasoning systems called logical case memory systems. The development of the underlying concepts has been driven by investigations in certain problems of case-based learning. Therefore, the present development of the target concepts is accompanied by an in-depth discussion of related learning problems. Logical ...
متن کاملThe educational function of Hosseiniyahs in promoting and perpetuating the Shiite lifestyle (Case study: Hosseiniyahs of Kashan)
Many philosophers believe that lifestyle is fundamentally dependent on worldview and ideology. Thus, the emergence of a culture in the social dimension occurs when people's lifestyles are in line with common thinking. Using the concept of guardianship along with Islamic monotheism, the Shiite school offers a practical program for all individual and social aspects of Shiites. In this program, re...
متن کاملHomotopy Type Theory: Univalent Foundations of Mathematics
Homotopy type theory is a new branch of mathematics, based on a recently discovered connection between homotopy theory and type theory, which brings new ideas into the very foundation of mathematics. On the one hand, Voevodsky's subtle and beautiful"univalence axiom"implies that isomorphic structures can be identified. On the other hand,"higher inductive types"provide direct, logical descriptio...
متن کاملTowards a Logic-Based Framework for Analyzing Stream Reasoning
The rise of smart applications has drawn interest to logical reasoning over data streams. Recently, different query languages and stream processing/reasoning engines were proposed in different communities. However, due to a lack of theoretical foundations, the expressivity and semantics of these diverse approaches were given only informally. Towards clear specifications and means for analytic s...
متن کامل