Human verifications: Computable with truth values outside logic

Area of Science:

• Cognitive Science
• Logic
• Computational Theory

Background:

• Verification is often viewed as a computation where descriptions matching reality are true.
• Controversy exists regarding whether human verification is computable, with Gödel and Penrose arguing against it.
• The theory of mental models proposes computability but finds standard true/false logic insufficient.

Purpose of the Study:

• To investigate the computability of human verification of disjunctive assertions.
• To explore whether standard logical truth values are sufficient for human verification.
• To examine the role of counterfactuals in verification processes.

Main Methods:

• Conducted three online experiments (n=208) on participants' verification of disjunctive statements (e.g., 'You arrived at Exeter or Perth').
• Analyzed how observations and the status of alternative possibilities influenced verification judgments.
• Implemented a computer program to model disjunctions and verify them using observed truth values.

Main Results:

• Verification depended on observed matches and the status of other potential locations.
• Participants utilized nuanced truth values beyond simple true/false, reflecting possibilities and impossibilities.
• Specific truth values incorporating counterfactuals were observed when destinations were reached or impossible.

Conclusions:

• Human verification of disjunctive assertions appears computable, utilizing truth values beyond standard binary logic.
• Mental models incorporating counterfactual reasoning are essential for understanding these verification processes.
• The computability of the awareness of a verification's outcome remains an open research question.