Constructive Negations and ParaconsistencySpringer Science & Business Media, 19.03.2008 - 242 Seiten Here is an account of recent investigations into the two main concepts of negation developed in the constructive logic: the negation as reduction to absurdity, and the strong negation. These concepts are studied in the setting of paraconsistent logic. |
Inhalt
| 1 | |
Minimal Logic Preliminary Remarks | 15 |
Logic of Classical Refutability | 31 |
The Class of Extensions of Minimal Logic | 41 |
Adequate Algebraic Semantics for Extensions | 57 |
Negatively Equivalent Logics | 81 |
15 | 93 |
Absurdity as Unary Operator | 101 |
21 | 126 |
Semantical Study of Paraconsistent Nelsons Logic | 131 |
N4Lattices | 159 |
The Class of N4Extensions | 177 |
Conclusion | 223 |
| 229 | |
| 237 | |
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According allows arbitrary Assume assumption axioms belongs C-presentation chapter characterization classical closed condition congruence Consequently consider constructive contains contradiction Corollary counterparts define definition denote determined direct easily element embedding equality equivalent exactly explosive extensions fact Figure filter finite follows formula fragment Further Heyting algebra holds homomorphism identity immediately implicative lattice In(p inclusion interpretation interval intuitionistic intuitionistic logic inverse isomorphic Item j-algebra language latter least Lemma mapping means minimal logic modal Moreover N4'-lattice natural negation negative negatively equivalent normal Note obtain operator ordering paraconsistent positive presentation Proof Proposition propositional variables provable prove relation respectively rule satisfying semantics set of formulas Spec(L1 strong structure subdirectly irreducible Take Theorem turns twist-structure valuation variety whence
Beliebte Passagen
Seite 229 - Die formalen Regeln der intuitionistischen Logik, Sitzungsber. Preuss. Akad. Wiss. (Phys. math.
Seite ii - ... Germany SCOPE OF THE SERIES Trends in Logic is a bookseries covering essentially the same area as the journal Studia Logica - that is, contemporary formal logic and its applications and relations to other disciplines. These include artificial intelligence, informatics, cognitive science, philosophy of science, and the philosophy of language. However, this list is not exhaustive, moreover, the range of applications, comparisons and sources of inspiration is open and evolves over time. Volume Editor...
Seite 235 - NN Vorob'ev. The problem of deducibility in constructive propositional calculus with strong negation. Doklady Akademii Nauk SSSR, 85, 1952, 689-692 (in Russian).
Seite 233 - AP Pynko. Functional completeness and axiomatizability within Belnap's four-valued logic and its expansions. Journal of Applied Non-classical Logics, 9, No.
Seite 235 - G. Wagner. Vivid logic. Knowledge-based reasoning with two kinds of negation. Springer LNAI 764, 1994.
Seite 229 - V. Goranko. The Craig interpolation theorem for propositional logics with strong negation. Studia Logica, 44, No.