{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,28]],"date-time":"2026-01-28T10:07:13Z","timestamp":1769594833844,"version":"3.49.0"},"reference-count":31,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2024,3,6]],"date-time":"2024-03-06T00:00:00Z","timestamp":1709683200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,3,8]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>We develop a system of basic probability reasoning founded on two great logical concepts, Gentzen\u2019s natural deduction systems and Carnap\u2013Popper probability of sentences. Our system makes it possible to manipulate with probabilized sentences and justify their causal relationships: if probabilities of sentences $A$ and $B$ are in $[r,1]$ and $[s,1]$, respectively, then the probability of sentence $C$ belongs to $[t,1]$, i.e. $A^{r},B^{s}\\vdash C^{t}$, for $r,s,t\\in [0,1]$. We prove that our system is sound and complete with respect to the traditional Carnap\u2013Popper type probability semantics. This approach opens up a new perspective of proof-theoretic treatment of sentence probability, potentially allowing immediate algorithmic use of the pure syntactic convenience of natural deductions in programming.<\/jats:p>","DOI":"10.1093\/logcom\/exae007","type":"journal-article","created":{"date-parts":[[2024,3,6]],"date-time":"2024-03-06T16:13:34Z","timestamp":1709741614000},"source":"Crossref","is-referenced-by-count":1,"title":["Probability and natural deduction"],"prefix":"10.1093","volume":"35","author":[{"given":"Marija","family":"Bori\u010di\u0107 Joksimovi\u0107","sequence":"first","affiliation":[{"name":"Faculty of Organizational Sciences , University of Belgrade, Belgrade, 11000, Serbia"}]},{"given":"Neboj\u0161a","family":"Ikodinovi\u0107","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics , University of Belgrade, Belgrade, 11000, Serbia"}]},{"given":"Nenad","family":"Stojanovi\u0107","sequence":"additional","affiliation":[{"name":"Faculty of Science 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