Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
A logic for temporal conditionals and a solution to the Sea Battle Puzzle
Stockholm University, Faculty of Humanities, Department of Philosophy. University of Johannesburg, South Africa.ORCID iD: 0000-0002-0157-1644
2018 (English)In: Advances in Modal Logic / [ed] Guram Bezhanishvili, Giovanna D'Agostino, George Metcalfe, Thomas Studer, London: College Publications, 2018, p. 379-398Conference paper, Published paper (Refereed)
Abstract [en]

Temporal reasoning with conditionals is more complex than both classical temporal reasoning and reasoning with timeless conditionals, and can lead to some rather counter-intuitive conclusions. For instance, Aristotle’s famous “Sea Battle Tomorrow” puzzle leads to a fatalistic conclusion: whether there will be a sea battle tomorrow or not, but that is necessarily the case now. We propose a branching-time logic LTC to formalise reasoning about temporal conditionals and provide that logic with adequate formal semantics. The logic LTC extends the Nexttime fragment of CTL∗ , with operators for model updates, restricting the domain to only future moments where antecedent is still possible to satisfy. We provide formal semantics for these operators that implements the restrictor interpretation of antecedents of temporalized conditionals, by suitably restricting the domain of discourse. As a motivating example, we demonstrate that a naturally formalised in our logic version of the ‘Sea Battle’ argument renders it unsound, thereby providing a solution to the problem with fatalist conclusion that it entails, because its underlying reasoning per cases argument no longer applies when these cases are treated not as material implications but as temporal conditionals. On the technical side, we analyze the semantics of LTC and provide a series of reductions of LTC-formulae, first recursively eliminating the dynamic update operators and then the path quantifiers in such formulae. Using these reductions we obtain a sound and complete axiomatization for LTC, and reduce its decision problem to that of the modal logic KD.

Place, publisher, year, edition, pages
London: College Publications, 2018. p. 379-398
Series
Advances in Modal Logic ; 12
Keywords [en]
conditionals, temporal logic, restrictors, the Sea Battle Puzzle
National Category
Algebra and Logic
Identifiers
URN: urn:nbn:se:su:diva-164927ISBN: 978-1-84890-255-8 (print)OAI: oai:DiVA.org:su-164927DiVA, id: diva2:1280753
Conference
12th International Conference on Advances in Modal Logic (AiML'2018), Bern, Switzerland, August 27-31, 2018
Funder
Swedish Research Council, 2015-04388Available from: 2019-01-21 Created: 2019-01-21 Last updated: 2019-04-10Bibliographically approved

Open Access in DiVA

fulltext(759 kB)3 downloads
File information
File name FULLTEXT01.pdfFile size 759 kBChecksum SHA-512
39f26e2e062102cacc86eb5352470e0540595217e95f4dea0fc6efd0888bd9ce9b4051491c1a616d7b9b6f51a32797d3aef995a01861f59f06b67c41e2ef6c88
Type fulltextMimetype application/pdf

Search in DiVA

By author/editor
Goranko, Valentin
By organisation
Department of Philosophy
Algebra and Logic

Search outside of DiVA

GoogleGoogle Scholar
Total: 3 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

isbn
urn-nbn

Altmetric score

isbn
urn-nbn
Total: 16 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf