Theoretical Computer Science
On conjectures in orthocomplemented lattices
Artificial Intelligence
Lattice-theoretic models of conjectures, hypotheses and consequences
Artificial Intelligence
Determinization of fuzzy automata with membership values in complete residuated lattices
Information Sciences: an International Journal
Automata theory based on complete residuated lattice-valued logic: Pushdown automata
Fuzzy Sets and Systems
Automata theory based on complete residuated lattice-valued logic: A categorical approach
Fuzzy Sets and Systems
On the reducibility of hypotheses and consequences
Information Sciences: an International Journal
Lattice-valued fuzzy Turing machines: Computing power, universality and efficiency
Fuzzy Sets and Systems
Consequences and conjectures in preordered sets
Information Sciences: an International Journal
Bisimulations for fuzzy automata
Fuzzy Sets and Systems
Characterizations of complete residuated lattice-valued finite tree automata
Fuzzy Sets and Systems
Automata theory based on complete residuated lattice-valued logic: Turing machines
Fuzzy Sets and Systems
Simulation for lattice-valued doubly labeled transition systems
International Journal of Approximate Reasoning
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Trillas et al. [E. Trillas, S. Cubillo, E. Castineira, On conjectures in orthocomplemented lattices, Artificial Intelligence 117 (2000) 255-275] recently proposed a mathematical model for conjectures, hypotheses and consequences (abbr. CHCs), and with this model we can execute certain mathematical reasoning and reformulate some important theorems in classical logic. We demonstrate that the orthomodular condition is not necessary for holding Watanabe's structure theorem of hypotheses, and indeed, in some orthocomplemented but not orthomodular lattices, this theorem is still valid. We use the CHC operators to describe the theorem of deduction, the theorem of contradiction and the Lindenbaum theorem of classical logic, and clarify their existence in the CHC models; a number of examples is presented. And we re-define the CHC operators in residuated lattices, and particularly reveal the essential differences between the CHC operators in orthocomplemented lattices and residuated lattices.