Context-Dependent Plausibility Judgments

• Context-dependent plausibility judgments are a flexible measure of explanatory adequacy that assesses how well hypotheses ‘force’ observed facts within varying contexts.
• The framework integrates abductive reasoning, biconditional inference, and neural network modeling to quantify context-sensitive explanatory effects.
• Its algebraic and operational properties enable robust reasoning in experimental analysis, inductive learning, and adaptive AI system design.

Context-dependent plausibility judgments concern the quantification, modeling, and operationalization of how the plausibility of hypotheses, explanations, or information is shaped by, and varies with, the surrounding context—be it observed data, semantic relations, environmental conditions, conversational history, or the framing of queries. This concept plays a central role in scientific inference, artificial intelligence, trust modeling, computational linguistics, and the design of robust reasoning systems, as it extends beyond classical probability and necessity to capture flexible, abductive, and often non-exclusive explanatory adequacy in varying contexts.

1. Foundational Definitions and Theoretical Characterization

Plausibility, within the domain of data interpretation, is defined as a context-sensitive measure of how effectively a hypothesis accounts for a set of observed propositions. Rather than simply counting frequencies or relying on event exclusivity (as in probability theory), a hypothesis A is evaluated for the proportion of contextual facts C it “forces” to be true or false, regardless of the number or mutual exclusivity of alternative explanations. The canonical scale for plausibility ranges over $[-1, 1]$, with %%%%1%%%% indicating complete plausibility (X fully explains the data), $pl(X) = 0$ denoting irrelevance, and $pl(X) < 0$ specifying that X is plausibly false.

Distinctive mathematical features of plausibility, particularly in context-dependent scenarios, include:

• Non-exclusiveness: The sum of plausibilities for incompatible hypotheses may exceed unity, reflecting the capacity for multiple, mutually exclusive candidates to each explain large portions of the data.
• Non-self-duality: The plausibility of X is not simply the complement of the plausibility of its negation; negative plausibility directly quantifies plausible falsity ($pl(-X) = -pl(X)$).
• Independence from Set Partitioning: Plausibility is unaffected by the cardinality or exclusivity of alternative explanations, making it robust under context expansion or contraction.

This contrasts sharply with probability ($P(X \cap Y) = P(X)P(Y)$ if independent) and with possibility measures (max-min algebra; $pos(X \lor Y) = max(pos(X), pos(Y))$; $pos(X \land Y) \leq min(pos(X), pos(Y))$). The Dempster-Shafer framework offers a relational view: $bel(X) \leq P(X) \leq pl(X)$ with $pl(X) = 1 - bel(-X)$, but is considered subjective with respect to mass assignments. The abduction-centric measure developed here ties plausibility directly to explanatory effect, emphasizing context-sensitive “forcing” rather than allocation of belief masses.

2. Plausibility, Abduction, and Biconditional Inference

Abductive reasoning is the process of formulating the most plausible explanation for a set of observed facts given their contextual constraints. In this paradigm, a hypothesis is plausible to the extent that it “forces” as many known contextual facts as possible (i.e., predicts or entails the context). The metric is inherently context-dependent, as the explanatory sufficiency of a hypothesis changes with the profile of the evidence.

Abduction’s deep connection to biconditionality is pivotal: when inference rules are interpreted as biconditional (i.e., A $\leftrightarrow$ C), abduction and deduction become duals, and context determines which direction is active. This biconditionality allows the plausibility calculus to relate naturally to rules of explanation, as in the Collins-Michalski theory, where generalization, specialization, analogy, and dependency can all be seen as bidirectional, context-mediated inferences.

In the probabilistic view, Bayesian updating ($P(\theta | x) = P(x | \theta)P(\theta)/P(x)$) is classically deductive, but, in abductive applications, the focus shifts to inverting explanatory relationships. While the author notes that naively substituting $P(\theta | x) \approx P(x | \theta)$ is not fully rational, the abductive perspective in plausibility seeks a measure of how sufficiently $\theta$ brings about $x$, bypassing the need for prior knowledge and emphasizing context-driven explanatory adequacy.

3. Algebraic and Operational Properties in Context

The operational calculus for context-dependent plausibility departs from standard additivity to emphasize combinatory and inferential flexibility. Explicitly:

• Addition-like properties: For hypotheses $A$ and $B$ with disjoint contextual effect, $pl(A \wedge B) = pl(A) + pl(B)$, while adjustments must be made for overlapping effect.
• Implication and disjunction: The plausibility of an implication is given as $pl(A_i \rightarrow A_j) = pl(A_j) - pl(A_i)$, capturing directional explanatory increments or decrements akin to learning rules in neural representations.
• Conjunction and disjunction operations do not necessarily preserve normalization, as mutual exclusiveness is not assumed.

This algebra supports robust reasoning in the presence of complex, context-sensitive datasets where overlaps, contradictions, and reinforcing cues coexist.

4. Neural Network Formalism and Computational Realization

Plausibility’s operationalization in computational models is illustrated via the wiring of logic into Hopfield neural networks. In this architecture:

• Neurons represent atomic propositions.
• Synaptic strengths encode logical relations corresponding to contextually constrained dependencies.
• Energy (Lyapunov) function minimization corresponds to the maximization of clause satisfaction, with the minimal energy state representing the most plausible explanation for the set of facts.

The plausibility metric is mapped to the number of satisfied versus unsatisfied contextual clauses. Concretely, if hypothesis $A_i$ induces network dynamics that produce few unsatisfied clauses (i.e., best fits the current context), $pl(A_i)$ is high. Hebbian learning mechanisms can be used to extract the logical structure from observed contexts and update synaptic weights accordingly, creating a tight context-explanation loop.

5. Comparative Frameworks: Probability, Possibility, and Dempster-Shafer

A synthesis of approaches demonstrates the position of plausibility in the landscape of uncertainty modeling:

Measure	Normalization	Context Interaction	Additivity/Compositionality
Probability	$\sum = 1$	Competing hypotheses	Additive (exclusive events)
Possibility	$\max = 1$	Max/min algebra	No sum constraint
Dempster-Shafer	$bel \leq P \leq pl$	Belief mass assignment	Subjective, set-theoretic
Plausibility (here)	None	Explanatory “forcing”	Non-exclusive, [-1,1] scale

Context-dependent plausibility prioritizes explanation over partitioning, interaction over isolation, and abductive coverage over mere frequency or possibility membership.

6. Relation to the Collins-Michalski Theory

The Collins-Michalski system introduces a multi-parameter approach to various types of inference—generalization, specialization, mutual implication, dependency, and analogy—each associated with uncertainty and graded acceptance. The context-dependent plausibility framework connects to this by interpreting these inferences, particularly mutual implication, as manifestations of biconditional abductive reasoning. By focusing on the degree to which hypotheses explain observed data, and emphasizing biconditionality, the new measure harmonizes with and generalizes the Collins-Michalski scheme.

7. Practical Implications and Interpretative Flexibility

The context-dependent approach to plausibility supports multiple use-cases:

• Experimental data analysis: It allows for direct comparison between competing hypotheses based on how well they explain the experimental context, regardless of the number of alternatives.
• Inductive learning and connectionist reasoning: By wiring logical structures into energy-based neural systems, plausibility assessments can be embedded in computational frameworks that learn and adapt as context evolves.
• Non-monotonic and default reasoning: Because plausibility is not strictly normalized, systems can flexibly revisit judgments as new context emerges, enabling iterative adjustment and revision.
• Generalization to evidence theories: While integrating Dempster-Shafer belief mass assignments, the context-dependent view restricts subjectivity by rooting plausibility in direct contextual “forcing,” offering a more objective abductive basis for evaluation.

The core significance lies in offering a non-probabilistic, non-possibilistic, but rigorous measure for plausibility that is maximally sensitive to the context of observed data, the structure of explanatory candidates, and the logic of hypothesis formation and evaluation.

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This conceptual and technical framework thus reconciles abductive, Bayesian, and neural perspectives on explanation. It enables robust, context-aware plausibility judgments for both symbolic and connectionist reasoning systems, with extensible implications for cognitive modeling, AI inference, and experimental data interpretation.