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ISABELLE - THE NEXT 700 THEOREM PROVERS [PDF]
, 1988 Isabelle is a generic theorem prover, designed for interactive reasoning in a variety of formal theories. At present it provides useful proof procedures for Constructive Type Theory, various first-order logics, Zermelo-Fraenkel set theory, and higher ...
PAULSON, LC
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A consistent foundation for Isabelle/HOL [PDF]
, 2015 The interactive theorem prover Isabelle/HOL is based on well understood Higher-Order Logic (HOL), which is widely believed to be consistent (and provably consistent in set theory by a standard semantic argument).
A Anand +20 more
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(In)consistency of Extensions of Higher Order Logic and Type Theory [PDF]
, 2007 It is well-known, due to the work of Girard and Coquand, that adding polymorphic domains to higher order logic, HOL, or its type theoretic variant ¿HOL, renders the logic inconsistent. This is known as Girard’s paradox, see [4]. But there is also another presentation of higher order logic, in its type theoretic variant called ¿PRED¿, to which ...
openaire +3 more sources
Foundational, compositional (co)datatypes for higher-order logic: category theory applied to theorem proving [PDF]
, 2012 Interactive theorem provers based on higher-order logic (HOL) traditionally follow the definitional approach, reducing high-level specifications to logical primitives. This also applies to the support for datatype definitions.
Blanchette, Jasmin +2 more
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Mechanizing Principia Logico-Metaphysica in Functional Type Theory
, 2019 Principia Logico-Metaphysica contains a foundational logical theory for metaphysics, mathematics, and the sciences. It includes a canonical development of Abstract Object Theory [AOT], a metaphysical theory (inspired by ideas of Ernst Mally, formalized ...
Benzmüller, Christoph +2 more
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A Paraconsistent Higher Order Logic [PDF]
, 2003 Classical logic predicts that everything (thus nothing useful at all) follows from inconsistency. A paraconsistent logic is a logic where an inconsistency does not lead to such an explosion, and since in practice consistency is difficult to achieve there
A. Church +18 more
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Adequate encodings of logical systems in UTT [PDF]
, 2003 In this paper, we present an existing and formalized type theory (UTT) as a logical framework. We compare the resulting framework with LF and give the representation of two significant type systems in the framework: the typed lambda calculus which ...
Mylonakis Pascual, Nicolás
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Practical Theory Extension in Event-B [PDF]
, 2013 . The Rodin tool for Event-B supports formal modelling and proof using a mathematical language that is based on predicate logic and set theory. Although Rodin has in-built support for a rich set of operators and proof rules, for some application areas ...
Butler, Michael, Maamria, Issam
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Counter Simulations via Higher Order Quantifier Elimination: a preliminary report [PDF]
, 2017 Quite often, verification tasks for distributed systems are accomplished via counter abstractions. Such abstractions can sometimes be justified via simulations and bisimulations.
Ghilardi, Silvio, Pagani, Elena
core +2 more sources