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We finally present algorithms for both approaches, which are based on generalizations of recent techniques for probabilistic logic programming under logical entailment.
The algorithm for the first approach still produces quite large weighted entropy maximization problems, while the one for the second approach generates optimization problems of the same size as the ones produced in probabilistic logic programming under logical entailment.
Of course, we need not and should not interpret Spinoza's following-from relation as the strict logical entailment of contemporary modal logic.
To capture this idea formally in deductive logic, we're equating prediction with logical entailment.
Hence Spinoza must believe that dependence and explanation are more fine-grained affairs than our modern logical entailment allows, since according to the latter, every necessary proposition entails and is entailed by every other necessary proposition.
Dreams defy logical entailment and narrative coherence, for they intermingle the residues of immediate daily experience with the deepest, often most infantile wishes.
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Relational biologists describe logical entailments in their mathematical work that represent entailments from the physical world and insist, for a correct modelling relation to be obtained, that these entailments must occur in the model.
Each major ontology redesign (including mapping) step is checked by a description logics reasoner, the results of which are then analysed and corrected under two perspectives: first, the classes tagged as 'inconsistent' are identified and the causes are investigated and repaired; second, every time the ontology has reached a consistent state, the logical entailments are analysed for adequacy.
If one accepts naive truth theory (or naive set theory), then Curry's paradox becomes a direct challenge to one's theory of logical implication or entailment.
Reichenbach's own presentation is a nearly impenetrable mix of conditions on truth, entailment, logical form, and verifiability, which surely contributed to its lack of influence.
Now, the deductive-logical notions of entailment and refutation (contradiction) exhibit the following well-known properties: Contraposition of entailment Entailment is contrapositive, but not commutative.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com