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VU Research PortalSuperposition for HigherOrder Logic
Bentham, Alexander; Blanchet, Jasmin; Turret, Sophie; Vukmirovi, Petarpublished in
Journal of Automated Reasoning
2023
DOI (link to publisher)
10.1007/s10817022096499
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How to fill out superposition for higher-order logic
How to fill out superposition for higher-order logic
01
Understand the basic principles of higher-order logic.
02
Identify the premises and conclusion of the argument you are trying to prove using superposition.
03
Convert the premises and conclusion into clause form.
04
Apply the superposition rule to combine the premises and derive the conclusion.
05
Use unification to resolve any conflicts or contradictions that arise during the superposition process.
06
Check the validity of the derived conclusion and make any necessary revisions.
07
Repeat the superposition process until a valid conclusion is reached.
Who needs superposition for higher-order logic?
01
Researchers and academics in the field of logic and mathematics who are studying higher-order logic.
02
Professionals working in artificial intelligence, automated reasoning, or formal verification.
03
Anyone interested in formal methods and automated theorem proving.
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What is superposition for higher-order logic?
Superposition for higher-order logic is a method used in automated theorem proving that allows for the reasoning about statements involving higher-order predicates and quantifiers. It extends the classical superposition method used in first-order logic to handle the complexities of higher-order statements.
Who is required to file superposition for higher-order logic?
Typically, researchers, mathematicians, or professionals working in fields related to formal logic and automated reasoning are required to file superposition for higher-order logic. This may include those working on projects that involve theorem proving or formal verification.
How to fill out superposition for higher-order logic?
To fill out superposition for higher-order logic, one must first express the higher-order logic statements accurately, identify the axioms and inference rules applicable, and then demonstrate the superposition steps leading to a conclusion. This process usually involves formal proof techniques and may require software tools designed for this purpose.
What is the purpose of superposition for higher-order logic?
The purpose of superposition for higher-order logic is to provide a complete and sound method for reasoning about higher-order statements, enabling the automated proving of theorems and the verification of logical arguments within a structured framework.
What information must be reported on superposition for higher-order logic?
Information that must be reported on superposition for higher-order logic typically includes the original higher-order statements, axioms used, steps taken in the proof process, and the final conclusions drawn from the reasoning.
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