Inference Space Search

Input: $ARGUMENTS

Interpretations

Before executing, identify which interpretation matches the user’s input:

Interpretation 1 — Draw conclusions from evidence: The user has a set of facts, observations, or data and wants to systematically generate and rank all valid inferences — deductive, inductive, abductive, and analogical. Interpretation 2 — Explore implications of a claim or decision: The user has a specific proposition and wants to understand what follows from it — consequences, prerequisites, and hidden entailments. Interpretation 3 — Find the best explanation for a puzzling observation: The user has something surprising or unexplained and wants to generate and evaluate competing explanations (primarily abductive reasoning).

If ambiguous, ask: “I can help with drawing conclusions from your evidence, exploring what follows from a claim, or finding the best explanation for something puzzling — which fits?” If clear from context, proceed with the matching interpretation.

Overview

Information implies other information. But not all inferences are equal:

• Some are logically valid, some aren’t
• Some have true premises, some don’t
• Some are useful, some are trivial

Generate the inference space, then filter by quality criteria.

Goal

From given information, generate all possible inferences, then search for those that are valid, sound, and useful.

Steps

Step 1: List Premises

Explicitly state all known facts/assumptions being used. Number them for reference. Note which are certain vs assumed.

Output: Numbered premise list

Step 2: Generate Deductive Inferences

What follows necessarily from the premises?

Apply:

• Modus ponens (If A then B; A; therefore B)
• Modus tollens (If A then B; not B; therefore not A)
• Syllogisms
• Instantiation of universals

Output: Deductive inferences

Step 3: Generate Inductive Inferences

What patterns can be generalized? What trends can be extrapolated?

Look for:

• Repeated observations
• Statistical patterns
• Historical trends

Output: Inductive inferences

Step 4: Generate Abductive Inferences

What would explain the premises? What causes would produce these effects?

For each surprising/unexplained fact:

• What could cause it?
• Which cause is simplest?
• Which is most likely given background knowledge?

Output: Abductive inferences

Step 5: Generate Analogical Inferences

What similar cases exist? What can be transferred from them?

For each premise about X:

• What is similar to X?
• Does the similar thing have relevant properties?
• Would those properties transfer?

Output: Analogical inferences

Step 6: Check Validity

For each inference, ask: “If the premises were true, would the conclusion have to be true?”

Score:

• 10: Necessarily follows (deductive, valid)
• 7-9: Highly probable (strong inductive)
• 4-6: Plausible (weak inductive, abductive)
• 1-3: Speculative (analogical, weak)

Output: Validity scores

Step 7: Check Soundness

For each inference, ask: “Are all the premises actually true?”

Check each premise used:

• Evidence for premise
• Confidence level
• Alternative interpretations

Output: Soundness assessment

Step 8: Check Usefulness

For each valid and sound inference, ask:

• Is it non-trivial? (tells us something new)
• Is it relevant? (matters for our purposes)
• Is it actionable? (suggests what to do)

Output: Usefulness scores

Step 9: Rank and Select

Combine scores: Validity × Soundness × Usefulness Rank inferences. Select top inferences for use.

Output: Ranked inferences

When to Use

• Drawing conclusions from evidence
• Reasoning about implications
• Finding hidden connections
• Building arguments
• Understanding consequences

Verification

• Premises are explicitly stated
• Multiple inference types were attempted
• Validity was assessed for each
• Soundness was assessed for each
• Usefulness was considered
• Top inferences are actionable