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Interpretations and extensions of many-sorted Universal Horn theories

By Pynko, Alexej P.

Interpretations and extensions of many-sorted Universal Horn theories

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Description
We elaborate a general theory of many-sorted algebraic structures as well as universal Horn theories both with and without equality on a uniform formal basis. We then study the issues of interpretability, equivalence, algebraic semantics, extensions, disjunctivity and deduction theorem within that general framework. We argue that not merely equivalence but equally interpretability properly retains extensions of Universal Horn theories. As a generic application, we develop a general theory of sequent calculi of various known kinds showing, among other things, existence of lattice-based algebraic semantics for any sequent calculi with basic structural rules (Enlargement, Permutation and Contraction). In addition, we apply our general elaboration to study many-valued paraconsistent logics (in particular, their maximal paraconsistency). Finally, we exemplify our general study by investigating certain propositional calculi of both Hilbert and Gentzen types.
Product details
Binding:
Paperback
Number of Pages:
376
Release Date:
2025-11-03
Publication Date:
2025-11-03
Publisher:
LAP LAMBERT Academic Publishing
Languages:
Original: English
ISBN10:
6209198074
ISBN13:
9786209198076
Weight:
578 g
Height:
150 cm
Width:
220 cm
Thickness:
23 cm
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