Abstract
This paper is a brief continuation of earlier work by the same authors [4] and [5] that deals with the concepts of conjecture, hypothesis and consequence in orthocomplemented complete lattices. It considers only the following three points: 1. Classical logic theorems of both deduction and contradiction are reinterpreted and proved by means of one specific operator C^ defined in [4]. 2. Having shown that there is reason to consider the set C^(P) of consequences of a set of premises P as too large, it is proven that C^(P) is the largest set of consequences that can be assigned to P by means of a Tarski's consequences operator, provided that T is a Boolean algebra. 3. On the other hand, it is proven that, also in a Boolean algebra, the set Φ^(P) of strict conjectures is the smallest of any Φ(P) such that P ⊆ Φ(P) and th at if P ⊆Q then Φ(Q) ⊆ Φ(P).
Paper partially supported by SpanishM inistry of Education and Culture under projects PB98-1379-C02-C02 and CICYT-TIC99-1151
∧P = Inf(P) = p^ and ∨P = Sup(P) = p^.
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Fernandez Pineda, A., Trillas, E., Vaucheret, C. (2001). Additional Comments on Conjectures, Hypotheses, and Consequences in Orthocomplemented Lattices. In: Campbell, J.A., Roanes-Lozano, E. (eds) Artificial Intelligence and Symbolic Computation. AISC 2000. Lecture Notes in Computer Science(), vol 1930. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44990-6_8
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DOI: https://doi.org/10.1007/3-540-44990-6_8
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