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Copy file name to clipboardExpand all lines: data.yaml
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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),
159
+
covering soundness and completeness w.r.t. possible world semantics and featuring a prototype of a theorem prover for GL itself.
160
+
The strategy we develop here to formalise the modal completeness proof overcomes the technical difficulty due to the non-compactness of GL
161
+
and is an adaptation—according to the formal language and tools at hand—of the proof given in George Boolos' 1995 monograph.
162
+
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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