With the fail-proof logic of the desperate, I resolved to enclose all three of us in the nearest bathroom.
Truth demands that you independently bear the burden of proof, logic and facts, and make up your own mind.
A dynamic proof for an adaptive logic of inductive generalizations may look as follows: The last column of each line of the proof contains its condition, i.e., a set of abnormalities Υ that encodes the assumptions used to derive the formula in the second column of the line: each υ ∈ Υ is assumed to be false.
If a characteristica universalis or ideal logical language could thus be created, we would have a system that could function not only as an international language and scientific notation but also as a calculus ratiocinator that provided both a logic of proof and a logic of discovery.
The Grundgesetze contains all the essential steps of a valid proof (in second-order logic) of the fundamental propositions of arithmetic from a single consistent principle.
In the TS we also witness the appearance, for the first time in the history of logic, of proof trees, i.e. diagrams showing the dependence of theorems on their grounds, axioms and auxiliary truths.
The proof of the theorem is written in a somewhat unusual form, interspersed with comments which I think mostly distract from the logic of the proof.
A resolution based proof system for a Temporal Logic of Possible Belief is presented.
As part of a project to provide a constructive semantics for intuitionistic logic, a formal logic of explicit proof terms was presented in Artemov 2001.
The logic of a proof in Taylor and Muller ([ 16] equations 2.1-2.13 and surrounding text) guarantees that accurate confidence regions are provided by the point-wise calculations.
It took Kleene realizability (Kleene 1945, Troelstra 1998) to reveal the computational semantics of Intuitionistic Logic and the Logic of Proofs to provide exact BHK semantics of proofs for Intuitionistic and Modal Logic.
