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@@ -155,15 +155,15 @@ Maggesi Perini-Brogi 2023:
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doi: 10.1007/s10817-023-09677-z
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repository: jrh13/hol-light/GL
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description: |
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We introduce our implementation in HOL Light of the metatheory for Gödel-Löb provability logic (GL),
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covering soundness and completeness w.r.t. possible world semantics and featuring a prototype of a theorem prover for GL itself.
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The strategy we develop here to formalise the modal completeness proof overcomes the technical difficulty due to the non-compactness of GL
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and is an adaptation—according to the formal language and tools at hand—of the proof given in George Boolos' 1995 monograph.
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Our theorem prover for GL relies then on this formalisation, is implemented as a tactic of HOL Light that mimics the proof search in the labelled sequent calculus G3KGL,
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and works as a decision algorithm for the provability logic:
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if the algorithm positively terminates, the tactic succeeds in producing a HOL Light theorem stating that the input formula is a theorem of GL;
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if the algorithm negatively terminates, the tactic extracts a model falsifying the input formula.
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We discuss our code for the formal proof of modal completeness and the design of our proof search algorithm.
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We introduce our implementation in HOL Light of the metatheory for Gödel-Löb provability logic (GL),
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covering soundness and completeness w.r.t. possible world semantics and featuring a prototype of a theorem prover for GL itself.
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The strategy we develop here to formalise the modal completeness proof overcomes the technical difficulty due to the non-compactness of GL
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and is an adaptation—according to the formal language and tools at hand—of the proof given in George Boolos' 1995 monograph.
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Our theorem prover for GL relies then on this formalisation, is implemented as a tactic of HOL Light that mimics the proof search in the labelled sequent calculus G3KGL,
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and works as a decision algorithm for the provability logic:
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if the algorithm positively terminates, the tactic succeeds in producing a HOL Light theorem stating that the input formula is a theorem of GL;
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if the algorithm negatively terminates, the tactic extracts a model falsifying the input formula.
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We discuss our code for the formal proof of modal completeness and the design of our proof search algorithm.
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Furthermore, we propose some examples of the latter’s interactive and automated use.
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tags:
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- modal logic
@@ -176,11 +176,11 @@ FormalizedFormalLogic/Foundation:
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github: iehality
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- name: Mashu Noguchi
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github: SnO2WMaN
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language: Lean
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language: Lean4
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repository: https://github.com/FormalizedFormalLogic/Foundation
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description: |
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Lean4 formalization for overall of mathematical logic.
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Including:
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Including:
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- (classical | intuitionistic | intermediate) propositional logic
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- (classical | intuitionistic) first-order predicate logic / arithmetic / set theory
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- Gödel's Completeness Theorem
@@ -202,13 +202,26 @@ FormalizedFormalLogic/Foundation:
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FormalizedFormalLogic/NonClassicalModalLogic:
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title: FormalizedFormalLogic/NonClassicalModalLogic
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authors:
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authors:
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- name: Mashu Noguchi
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github: SnO2WMaN
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language: Lean
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language: Lean4
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repository: https://github.com/FormalizedFormalLogic/NonClassicalModalLogic
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description: |
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Lean4 Formalization of Non-classical modal logic: (intuitionistic | constructive) modal logic.
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tags:
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- modal logic
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Lean4 Formalization of Non-classical modal logic: (intuitionistic | constructive) modal logic.
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tags:
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- modal logic
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ruplet/formalization-of-bounded-arithmetic:
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title: ruplet/formalization-of-bounded-arithmetic
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authors:
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- name: Paweł Balawender
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github: ruplet
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repository:
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url: https://github.com/ruplet/formalization-of-bounded-arithmetic
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description: |
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Formalizing bounded arithmetic and proof complexity and proof extraction.
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language: Lean4
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tags:
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- bounded arithmetic
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- computational complexity

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