PEF model

The Polemical Effectiveness Formula (PEF) is an advanced evaluative model designed to quantify the effectiveness of apologetic arguments within structured theological discourse. Developed as a complementary tool to the Kaedah Istifham Mantiqi (Method of Logical Inquiry), the PEF model offers Muslim apologists a systematic approach to assess how effectively their questioning exposes logical inconsistencies, moral vulnerabilities, and foundational clashes in opposing theological positions, particularly during engagements with Christian missionaries.

Formula

The PEF Score is calculated using the following weighted formula:

${\text{PEF Score}}=({\text{LP}}\times 0.30)+({\text{MV}}\times 0.30)+({\text{FC}}\times 0.25)+({\text{RR}}\times 0.15)$

Where:

• LP = Logical Pressure
• MV = Moral Vulnerability
• FC = Foundational Clash
• RR = Resistance Response

Each variable is rated on a scale from 1 to 10 based on observed debate dynamics.

Derived metrics

The PEF model includes additional metrics to evaluate the broader impact and sustainability of polemical arguments.

Probability of Persuasion

This metric estimates the likelihood of influencing the audience or opponent based on the PEF Score.

Failed to parse (syntax error): {\displaystyle \text{Probability (\%)} = \left( \frac{\text{PEF Score}}{10} \right) \times 100 }

Effective pressure

Accounts for the time decay of argument impact over prolonged discourse or multiple debate rounds.

${\text{Effective Pressure}}={\text{PEF Score}}\times e^{-kt}$

Where:

• k = Decay constant
• t = Time elapsed (in hours) or number of reply rounds

Force magnitude

Represents the total polemical force exerted, focusing on logical, moral, and foundational dimensions.

$|{\vec {F}}|={\sqrt {{\text{LP}}^{2}+{\text{MV}}^{2}+{\text{FC}}^{2}}}$

Rhetorical Work done

Measures the actual rhetorical impact in terms of shifting audience perception.

${\text{Work}}=|{\vec {F}}|\times \Delta B$

Where:

• ΔB = Belief displacement (rated from 0 to 1)

Application

The PEF model is primarily used in conjunction with structured questioning techniques, allowing apologists to evaluate both the immediate and sustained effectiveness of their arguments. By applying these metrics, practitioners can refine their approach in live debates, written exchanges, or post-discussion analyses.