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.

Scoring guidelines

Each component of the PEF formula is rated on a scale from 1 to 10. The following table guides how to assign these values based on debate performance:

Score	Logical Pressure (LP)	Moral Vulnerability (MV)	Foundational Clash (FC)	Resistance Response (RR)
10	Exposes undeniable core contradictions.	Reveals fatal moral flaws undermining the argument.	Demonstrates total irreconcilability between worldviews.	Opponent resorts to complete evasion or emotional reactions.
9	Forces major concessions due to clear inconsistencies.	Highlights severe ethical double standards.	Shows critical doctrinal incompatibility.	Opponent heavily dodges or shifts topics frequently.
8	Identifies strong contradictions with partial admissions.	Exposes clear moral incoherence recognized by the audience.	Establishes significant theological divergence.	Noticeable rhetorical deflection or metaphor use.
7	Reveals contradictions, though opponent attempts weak justification.	Raises impactful ethical concerns.	Highlights key doctrinal differences, downplayed by opponent.	Mild dodging or indirect answers.
6	Detects minor inconsistencies needing further probing.	Points out ethical weaknesses without destabilizing the argument.	Shows foundational differences with some ambiguity.	Occasional evasive responses.
5	Presents potential tensions but opponent deflects confidently.	Raises peripheral moral issues.	Moderate differences with room for harmonization.	Balanced responses with minor hesitation.
4	Weak logical pressure; opponent responds strongly.	Moral critique lacks significant impact.	Differences are acknowledged but trivialized.	Smooth and confident responses.
3	Minimal challenge; speculative argumentation.	Ethical points appear forced or irrelevant.	Foundational differences poorly articulated.	Fully cooperative opponent.
2	Barely any logical impact.	No meaningful ethical critique.	Fails to highlight core doctrinal differences.	Open and confident engagement.
1	No logical relevance; incoherent questioning.	No moral critique introduced.	No attempt to address foundational issues.	Opponent dominates the exchange confidently.

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.

${\text{Probability}}~(\%)=\left({\frac {\text{PEF Score}}{10}}\right)\times 100$

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.