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We prove that counting satisfying assignments of propositional languages is intractable even for Horn and monotone formulae, and even when the size of clauses and number of occurrences of the variables are extremely limited. This should be contrasted with the case of deductive reasoning, where Horn theories and theories with binary clauses are distinguished by the existence of linear· time satisfiability algorithms. What is even more surprising is that, as we show, even approximating the number of satisfying assignments (i.e., \"approximating\" approximate reasoning), is intractable for most of these restricted theories. We also identify some restricted classes of propositional formulae for which we develop efficient algorithms for counting satisfying assignments.","doi":null,"url":"https://ijcai.org/proceedings/1993/86","pdf":"https://ijcai.org/proceedings/1993/0086.pdf","markdown":"https://ijcai.org/proceedings/1993/86.md","bibtex":"https://ijcai.org/proceedings/1993/bibtex/86","volume":{"slug":"1993","title":"Proceedings of the Thirteenth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 1993","url":"https://ijcai.org/proceedings/1993/","year":1993,"location":"Chambéry, France","dates":"","editors":"Ruzena Bajcsy","isbn":"","publisher":"International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":"Knowledge Representation","track":"Knowledge Representation","number":86,"pages":{"first":613,"last":618},"keywords":[],"videos":[],"references":[{"position":1,"raw":"[Bacchus et al., 1992] F . Bacchus , A. Grove, J. Y . Halpern , and D. Koller. 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