A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit <a rel="external noopener" href="http://pdfs.semanticscholar.org/fc62/d4b47d0da59b957a2e19b91c6edf4259bdef.pdf">the original URL</a>. The file type is <code>application/pdf</code>.
Cut-free sequent and tableau systems for propositional Diodorean modal logics
<span title="">1994</span>
<i title="Springer Nature">
<a target="_blank" rel="noopener" href="https://fatcat.wiki/container/nzzezfqw65bhpbeksnoskjzuza" style="color: black;">Studia Logica: An International Journal for Symbolic Logic</a>
</i>
Preserved Fulltext
We present sound, (weakly) complete and cut-free tableau systems for the propositional normal modal logics S4:3, S4:3:1 and S4:14. When the modality 2 is given a temporal interpretation, these logics respectively model time as a linear dense sequence of points; as a linear discrete sequence of points; and as a branching tree where each branch is a linear discrete sequence of points. Although cut-free, the last two systems do not possess the subformula property. But for any given nite set of
<span class="external-identifiers">
<a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/bf01057938">doi:10.1007/bf01057938</a>
<a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/snmgz5cr7fc6vnxthziv5quyq4">fatcat:snmgz5cr7fc6vnxthziv5quyq4</a>
</span>
more »
... ulae X the \superformulae" involved are always bounded by a nite set of formulae X L depending only on X and the logic L. Thus each system gives a nondeterministic decision procedure for the logic in question. The completeness proofs yield deterministic decision procedures for each logic because each proof is constructive. Each tableau system has a cut-free sequent analogue proving that Gentzen's cut-elimination theorem holds for these latter systems. The techniques are due to Hintikka and Rautenberg.
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190309163552/http://pdfs.semanticscholar.org/fc62/d4b47d0da59b957a2e19b91c6edf4259bdef.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext">
<button class="ui simple right pointing dropdown compact black labeled icon button serp-button">
<i class="icon ia-icon"></i>
Web Archive
[PDF]
<div class="menu fulltext-thumbnail">
<img src="https://blobs.fatcat.wiki/thumbnail/pdf/fc/62/fc62d4b47d0da59b957a2e19b91c6edf4259bdef.180px.jpg" alt="fulltext thumbnail" loading="lazy">
</div>
</button>
</a>
<a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/bf01057938">
<button class="ui left aligned compact blue labeled icon button serp-button">
<i class="external alternate icon"></i>
springer.com
</button>
</a>