{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,1,11]],"date-time":"2025-01-11T01:40:30Z","timestamp":1736559630894,"version":"3.32.0"},"publisher-location":"Berlin, Heidelberg","reference-count":29,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540454588"},{"type":"electronic","value":"9783540454595"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2006]]},"DOI":"10.1007\/11874683_16","type":"book-chapter","created":{"date-parts":[[2006,9,27]],"date-time":"2006-09-27T13:47:26Z","timestamp":1159364846000},"page":"240-255","source":"Crossref","is-referenced-by-count":3,"title":["Reasoning About States of Probabilistic Sequential Programs"],"prefix":"10.1007","author":[{"given":"R.","family":"Chadha","sequence":"first","affiliation":[]},{"given":"P.","family":"Mateus","sequence":"additional","affiliation":[]},{"given":"A.","family":"Sernadas","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"issue":"1","key":"16_CR1","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1006\/inco.1994.1049","volume":"112","author":"M. Abadi","year":"1994","unstructured":"Abadi, M., Halpern, J.Y.: Decidability and expressiveness for first-order logics of probability. Information and Computation\u00a0112(1), 1\u201336 (1994)","journal-title":"Information and Computation"},{"key":"16_CR2","doi-asserted-by":"publisher","first-page":"547","DOI":"10.1109\/SFCS.2000.892142","volume-title":"FOCS 2000: Proceedings of the 41st Annual Symposium on Foundations of Computer Science","author":"A. Ambainis","year":"2000","unstructured":"Ambainis, A., Mosca, M., Tapp, A., de Wolf, R.: Private quantum channels. In: FOCS 2000: Proceedings of the 41st Annual Symposium on Foundations of Computer Science, p. 547. IEEE Computer Society Press, Los Alamitos (2000)"},{"key":"16_CR3","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-05355-3","volume-title":"Algorithms in Real Algebraic Geometry","author":"S. Basu","year":"2003","unstructured":"Basu, S., Pollack, R., Marie-Fran\u00e7oise, R.: Algorithms in Real Algebraic Geometry. Springer, Heidelberg (2003)"},{"key":"16_CR4","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1016\/j.entcs.2006.04.003","volume":"158","author":"R. Chadha","year":"2006","unstructured":"Chadha, R., Mateus, P., Sernadas, A.: Reasoning about quantum imperative programs. Electronic Notes in Theoretical Computer Science\u00a0158, 19\u201340 (2006) (Invited talk at the Twenty-Second Conference on the Mathematical Foundations of Programming Semantics)","journal-title":"Electronic Notes in Theoretical Computer Science"},{"key":"16_CR5","unstructured":"Chadha, R., Mateus, P., Sernadas, A., Sernadas, C.: Extending classical logic for reasoning about quantum systems. CLC, Department of Mathematics, Instituto Superior T\u00e9cnico (preprint, 2005) (Invited submission to the Handbook of Quantum Logic)"},{"issue":"3","key":"16_CR6","doi-asserted-by":"publisher","first-page":"315","DOI":"10.1142\/S012905410200114X","volume":"13","author":"J.I. Hartog den","year":"2002","unstructured":"den Hartog, J.I., de Vink, E.P.: Verifying probabilistic programs using a hoare like logic. International Journal of Foundations of Computer Science\u00a013(3), 315\u2013340 (2002)","journal-title":"International Journal of Foundations of Computer Science"},{"issue":"1-2","key":"16_CR7","doi-asserted-by":"publisher","first-page":"78","DOI":"10.1016\/0890-5401(90)90060-U","volume":"87","author":"R. Fagin","year":"1990","unstructured":"Fagin, R., Halpern, J.Y., Megiddo, N.: A logic for reasoning about probabilities. Information and Computation\u00a087(1-2), 78\u2013128 (1990)","journal-title":"Information and Computation"},{"issue":"1\/2","key":"16_CR8","doi-asserted-by":"publisher","first-page":"11","DOI":"10.1016\/S0019-9958(84)80039-X","volume":"63","author":"Y.A. Feldman","year":"1984","unstructured":"Feldman, Y.A.: A decidable propositional dynamic logic with explicit probabilities. Information and Control\u00a063(1\/2), 11\u201338 (1984)","journal-title":"Information and Control"},{"key":"16_CR9","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1016\/0022-0000(84)90065-5","volume":"28","author":"Y.A. Feldman","year":"1984","unstructured":"Feldman, Y.A., Harel, D.: A probabilistic dynamic logic. Journal of Computer and System Sciences\u00a028, 193\u2013215 (1984)","journal-title":"Journal of Computer and System Sciences"},{"key":"16_CR10","doi-asserted-by":"publisher","first-page":"512","DOI":"10.1007\/BF01211866","volume":"6","author":"H. Hansson","year":"1995","unstructured":"Hansson, H., Jonsson, B.: A logic for reasoning about time and reliability. Formal Aspects of Computing\u00a06, 512\u2013535 (1995)","journal-title":"Formal Aspects of Computing"},{"key":"16_CR11","doi-asserted-by":"publisher","first-page":"576","DOI":"10.1145\/363235.363259","volume":"12","author":"C. Hoare","year":"1969","unstructured":"Hoare, C.: An axiomatic basis for computer programming. Communications of the ACM\u00a012, 576\u2013583 (1969)","journal-title":"Communications of the ACM"},{"key":"16_CR12","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511551574","volume-title":"Model Theory","author":"W. Hodges","year":"1993","unstructured":"Hodges, W.: Model Theory. Cambridge University Press, Cambridge (1993)"},{"key":"16_CR13","doi-asserted-by":"crossref","unstructured":"Huth, M., Kwiatkowska, M.: Quantitative analysis and model checking. In: 12th Annual IEEE Symposium on Logic in Computer Science (LICS 1997), pp. 111\u2013122 (1997)","DOI":"10.1109\/LICS.1997.614940"},{"key":"16_CR14","unstructured":"Jones, C.: Probabilistic Non-determinism. PhD thesis, U. Edinburgh (1990)"},{"key":"16_CR15","doi-asserted-by":"publisher","first-page":"186","DOI":"10.1109\/LICS.1989.39173","volume-title":"Proceedings of the Fourth Annual Symposium on Logic in Computer Science","author":"C. Jones","year":"1989","unstructured":"Jones, C., Plotkin, G.D.: A probabilistic powerdomain of evaluations. In: Proceedings of the Fourth Annual Symposium on Logic in Computer Science, pp. 186\u2013195. IEEE Computer Society Press, Los Alamitos (1989)"},{"key":"16_CR16","doi-asserted-by":"publisher","first-page":"328","DOI":"10.1016\/0022-0000(81)90036-2","volume":"22","author":"D. Kozen","year":"1981","unstructured":"Kozen, D.: Semantics of probabilistic programs. Journal of Computer System Science\u00a022, 328\u2013350 (1981)","journal-title":"Journal of Computer System Science"},{"key":"16_CR17","doi-asserted-by":"publisher","first-page":"162","DOI":"10.1016\/0022-0000(85)90012-1","volume":"30","author":"D. Kozen","year":"1985","unstructured":"Kozen, D.: A probabilistic PDL. Journal of Computer System Science\u00a030, 162\u2013178 (1985)","journal-title":"Journal of Computer System Science"},{"key":"16_CR18","unstructured":"Makowsky, J.A., Tiomkin, M.L.: Probabilistic propositional dynamic logic (manuscript, 1980)"},{"key":"16_CR19","doi-asserted-by":"crossref","unstructured":"Mateus, P., Sernadas, A.: Weakly complete axiomatization of exogenous quantum propositional logic. Information and Computation (to appear)","DOI":"10.1016\/j.ic.2006.02.001"},{"key":"16_CR20","unstructured":"Mateus, P., Sernadas, A., Sernadas, C.: Exogenous semantics approach to enriching logics. In: Essays on the Foundations of Mathematics and Logic. Advanced Studies in Mathematics and Logic, vol.\u00a01, pp. 165\u2013194. Polimetrica (2005)"},{"issue":"3","key":"16_CR21","doi-asserted-by":"publisher","first-page":"325","DOI":"10.1145\/229542.229547","volume":"18","author":"C. Morgan","year":"1996","unstructured":"Morgan, C., McIver, A., Seidel, K.: Probabilistic predicate transformers. ACM Transactions on Programming Languages and Systems\u00a018(3), 325\u2013353 (1996)","journal-title":"ACM Transactions on Programming Languages and Systems"},{"key":"16_CR22","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"216","DOI":"10.1007\/3-540-45793-3_15","volume-title":"Computer Science Logic","author":"M.A. Moshier","year":"2002","unstructured":"Moshier, M.A., Jung, A.: A logic for probabilities in semantics. In: Bradfield, J.C. (ed.) CSL 2002. LNCS, vol.\u00a02471, pp. 216\u2013231. Springer, Heidelberg (2002)"},{"key":"16_CR23","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"288","DOI":"10.1007\/3-540-49019-1_20","volume-title":"Foundations of Software Science and Computation Structures","author":"M. Narasimha","year":"1999","unstructured":"Narasimha, M., Cleaveland, W.R., Iyer, P.: Probabilistic temporal logics via the modal mu-calculus. In: Thomas, W. (ed.) FOSSACS 1999. LNCS, vol.\u00a01578, pp. 288\u2013305. Springer, Heidelberg (1999)"},{"issue":"1","key":"16_CR24","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1016\/0004-3702(86)90031-7","volume":"28","author":"N.J. Nilsson","year":"1986","unstructured":"Nilsson, N.J.: Probabilistic logic. Artificial Intelligence\u00a028(1), 71\u201387 (1986)","journal-title":"Artificial Intelligence"},{"issue":"1-2","key":"16_CR25","doi-asserted-by":"publisher","first-page":"39","DOI":"10.1016\/0004-3702(93)90167-A","volume":"59","author":"N.J. Nilsson","year":"1993","unstructured":"Nilsson, N.J.: Probabilistic logic revisited. Artificial Intelligence\u00a059(1-2), 39\u201342 (1993)","journal-title":"Artificial Intelligence"},{"key":"16_CR26","series-title":"Lecture Notes in Computer Science","first-page":"396","volume-title":"Proceedings of the Carnegie Mellon Workshop on Logic of Programs","author":"R. Parikh","year":"1983","unstructured":"Parikh, R., Mahoney, A.: A theory of probabilistic programs. In: Proceedings of the Carnegie Mellon Workshop on Logic of Programs. LNCS, vol.\u00a064, pp. 396\u2013402. Springer, Heidelberg (1983)"},{"key":"16_CR27","unstructured":"Ramshaw, L.H.: Formalizing the analysis of algorithms. PhD thesis, Stanford University (1979)"},{"key":"16_CR28","doi-asserted-by":"crossref","unstructured":"Reif, J.H.: Logics for probabilistic programming (extended abstract). In: STOC 1980: Proceedings of the Twelfth Annual ACM Symposium on Theory of Computing, pp. 8\u201313 (1980)","DOI":"10.1145\/800141.804647"},{"key":"16_CR29","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.entcs.2004.06.063","volume":"129","author":"R. Tix","year":"2005","unstructured":"Tix, R., Keimel, K., Plotkin, G.D.: Semantic domains for combining probability and non-determinism. Electronic Notes in Theoretical Computer Science\u00a0129, 1\u2013104 (2005)","journal-title":"Electronic Notes in Theoretical Computer Science"}],"container-title":["Lecture Notes in Computer Science","Computer Science Logic"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/11874683_16.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,11]],"date-time":"2025-01-11T01:18:12Z","timestamp":1736558292000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/11874683_16"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006]]},"ISBN":["9783540454588","9783540454595"],"references-count":29,"URL":"https:\/\/doi.org\/10.1007\/11874683_16","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2006]]}}}