Abstract
We have applied an elegant and flexible logic embedding approach to verify and automate a prominent philosophical argument: the ontological argument for the existence of God. In our ongoing computer-assisted study, higher-order automated reasoning tools have made some interesting observations, some of which were previously unknown.
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C. Benzmüller—This work has been supported by the German Research Foundation DFG under grants BE2501/9-1,2 and BE2501/11-1.
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Notes
- 1.
Some Notes on THF, which is a concrete syntax for HOL: $i and $o represent the HOL base types i and o (Booleans). $i>$o encodes a function (predicate) type. Predicate application as in A(X, W) is encoded as ((A@X)@W) or simply as (A@X@W), i.e., function/predicate application is represented by @; universal quantification and \(\lambda \)-abstraction as in \(\lambda {A}_{i\rightarrow o} \forall {W_i} (A\,W)\) and are represented as in \(\mathtt{\hat{}}\)[X:$i>$o]:![W:$i]:(A@W); comments begin with %.
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Benzmüller, C., Paleo, B.W. (2015). On Logic Embeddings and Gödel’s God. In: Codescu, M., Diaconescu, R., Țuțu, I. (eds) Recent Trends in Algebraic Development Techniques. WADT 2015. Lecture Notes in Computer Science(), vol 9463. Springer, Cham. https://doi.org/10.1007/978-3-319-28114-8_1
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