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Transreal logical space of all propositions

dos Reis, T. S. and Anderson, J. (2015) Transreal logical space of all propositions. In: Kim, H. K., Amouzegar, M. A. and Ao, S.-l. (eds.) Transactions on Engineering Technologies, World Congress on Engineering and Computer Science 2014. Springer Netherlands, pp. 227-242.

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To link to this item DOI: 10.1007/978-94-017-7236-5


Transreal numbers provide a total semantics containing classical truth values, dialetheaic, fuzzy and gap values. A paraconsistent Sheffer Stroke generalises all classical logics to a paraconsistent form. We introduce logical spaces of all possible worlds and all propositions. We operate on a proposition, in all possible worlds, at the same time. We define logical transformations, possibility and necessity relations, in proposition space, and give a criterion to determine whether a proposition is classical. We show that proofs, based on the conditional, infer gaps only from gaps and that negative and positive infinity operate as bottom and top values.

Item Type:Book or Report Section
Divisions:Science > School of Mathematical, Physical and Computational Sciences > Department of Computer Science
ID Code:43185
Uncontrolled Keywords:all possible worlds, logical spaces, multi-valued logics, paraconsistent logics, transreal numbers, total semantics.
Publisher:Springer Netherlands


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