A Logic for Probabilities in Semantics [chapter]

M. Andrew Moshier, Achim Jung
<span title="">2002</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
Probabilistic computation has proven to be a challenging and interesting area of research, both from the theoretical perspective of denotational semantics and the practical perspective of reasoning about probabilistic algorithms. On the theoretical side, the probabilistic powerdomain of Jones and Plotkin represents a significant advance. Further work, especially by Alvarez-Manilla, has greatly improved our understanding of the probabilistic powerdomain, and has helped clarify its relation to
more &raquo; ... ssical measure and integration theory. On the practical side, many researchers such as Kozen, Segala, Desharnais, and Kwiatkowska, among others, study problems of verification for probabilistic computation by defining various suitable logics for the classes of processes under study. The work reported here begins to bridge the gap between the domain theoretic and verification (model checking) perspectives on probabilistic computation by exhibiting sound and complete logics for probabilistic powerdomains that arise directly from given logics for the underlying domains. The category in which the construction is carried out generalizes Scott's Information Systems by taking account of full classical sequents. Via Stone duality, following Abramsky's Domain Theory in Logical Form, all known interesting categories of domains are embedded as subcategories. So the results reported here properly generalize similar constructions on specific categories of domains. The category offers a promising universe of semantic domains characterized by a very rich structure and good preservation properties of standard constructions. Furthermore, because the logical constructions make use of full classical sequents, the morphisms have a natural non-deterministic interpretation. Thus the category is a natural one in which to investigate the relationship between probabilistic and non-deterministic computation. We discuss the problem of integrating probabilistic and non-deterministic computation after presenting the construction of logics for probabilistic powerdomains.
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-45793-3_15">doi:10.1007/3-540-45793-3_15</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/j2jzttl65be2vhr4m5zi4c6qy4">fatcat:j2jzttl65be2vhr4m5zi4c6qy4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20130903144530/http://www.cs.bham.ac.uk:80/~axj/pub/papers/Moshier-Jung-2002-A-logic-for-probabilities-in-semantics.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/2e/03/2e03f7ab59545497b5481fe4035b7940f85b80b7.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-45793-3_15"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>