<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>27</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Primiero, Giuseppe</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Intuitionistic Logic of Proofs with dependent proof terms</style></title><secondary-title><style face="normal" font="default" size="100%">Preprint Series of the Isaac Newton Institute for Mathematical Sciences</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2012</style></year></dates><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;The basic logic of proofs extends the usual propositional language by expressions of the form &quot;&lt;em&gt;s&lt;/em&gt; is a proof of &lt;em&gt;A&lt;/em&gt;&quot;, for any proposition &lt;em&gt;A&lt;/em&gt;. In this paper we explore the extension of its intuitionistic fragment to a language including expressions of the form &quot;&lt;em&gt;t&lt;/em&gt; is a proof of &lt;em&gt;B&lt;/em&gt;, dependent from &lt;em&gt;s&lt;/em&gt;being a proof of &lt;em&gt;A&lt;/em&gt;&quot;. We aim at laying down a ground comparison with equivalent constructions present in theories of dependent types, especially those similarly based on the Brouwer-Heyting-Kolmogorov semantics. We further translate this extended language to a natural deduction calculus which allows for a double interpretation of the construction on which a proof term may depend: as actually proven, or valid assumption, or as possibly proven, locally true assumption. We show meta-theoretical properties for this calculus and explain normalisation to a language with only unconditional proofs. We conclude by stating the characterization of our calculus with standard intutionistic logic of proofs&lt;/p&gt;</style></abstract></record></records></xml>