Formal logic
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Part III: Formal Logic & Philosophy (300-Level)
3.1 PyWhy/DoWhy Causal Inference and the Do-Calculus
The CoReason Manifest operationalizes Judea Pearl's Structural Causal Models (SCMs) to mathematically distinguish strict causation from statistical correlation. This capability is structurally defined within the EpistemicCausalGraphDefinitionState, which integrates directly with OSS DoWhy (PyWhy).
To explicitly manage confounding variables during inference, the profile partitions the topological space into observed_variables and latent_variables (unobserved confounders). To prevent memory exhaustion during graphical evaluation, both sets are restricted to a maximum of 1,000 nodes, with individual string names clamped by StringConstraints(max_length=255). Topological relationships between these nodes are mapped via the CausalDirectedEdgeState, where the causal connection is strictly confined to the edge_class Literal automaton: ["direct_cause", "confounder", "collider", "mediator"]. Causal paradoxes are physically blocked by the @model_validator reject_self_referential_edge, which mathematically guarantees that a source_variable cannot equal a target_variable.
When an agent must prove direct causal influence, it utilizes an DoWhyInterventionIntent to execute a DoWhy Do-Operator ($P(y|do(X=x))$). This task authorizes the orchestrator to compute the causal effect using the DoWhy Python library.
3.2 Truth Maintenance Systems and Epistemic Contagion
Autonomous agents operating in complex environments must perform non-monotonic reasoning—the capacity to retract previously held conclusions when foundational premises are falsified. The manifest handles belief revision using a Jon Doyle-style Truth Maintenance System (TMS), mathematically governed by the TruthMaintenancePolicy.
If a foundational axiom collapses, the system prevents epistemic contagion from ravaging the entire Merkle-DAG by emitting a DefeasibleCascadeEvent. This event actively severs downstream dependencies linked to the root_falsified_event_cid. The cascading Shannon Entropy reduction across these severed edges is governed by a propagated_decay_factor clamped between ge=0.0 and le=1.0.
To prevent this truth-maintenance cascade from triggering infinite recursion or unravelling the entire graph, the TruthMaintenancePolicy enforces absolute physical limits: max_cascade_depth and max_quarantine_blast_radius are strictly bound integers (gt=0, le=18446744073709551615). Furthermore, the quarantined_event_cids array within the cascade is deterministically sorted via a @model_validator to preserve RFC 8785 canonical hashing, while the reject_root_in_quarantine validator ensures the root falsified event is not paradoxically listed within its own quarantine subgraph.
3.3 Dung's Abstract Argumentation Framework
To algorithmically evaluate conflicting multi-agent claims, the ontology translates unstructured debate into Dung’s Abstract Argumentation Framework ($AF = \langle AR, \rightarrow \rangle$) via the EpistemicArgumentGraphState.
State-space explosion during dialectical processing is mitigated by capping the macroscopic adjacency matrix; both the claims dictionary (holding propositions) and the attacks dictionary (holding defeaters) are strictly limited to max_length=10000 keys.
Adversarial intersections between claims are mapped by the DefeasibleAttackEvent. This object projects a directed edge from a source_claim_cid to a target_claim_cid (both enforced as 128-character CID regex strings). The nature of the defeater is mathematically restricted by the AttackVectorProfile, which locks the attack_vector strictly to the literal automaton ["rebuttal", "undercutter", "underminer"]. By rendering arguments as algebraic matrices, the orchestrator can deterministically compute the conflict-free Grounded Extension of surviving truths.
3.4 The Curry-Howard Correspondence and Theorem Proving
To bridge the gap between probabilistic neural inference and mathematically verified truth, the system incorporates the Curry-Howard Correspondence—mapping pure logic to computational types—to form unassailable deductive chains via the EpistemicTopologicalProofManifest.
An agent submits a logical argument through the axiomatic_chain array (min_length=1). Because logical deduction requires a strict chronological sequence of steps to be valid, this array utilizes a coreason_topological_exemption inside its JSON schema. This explicit exemption bypasses the standard alphabetical array sorting mandated for cryptographic hashing elsewhere in the system, mathematically preserving the sequential order of the proof.
The outcome of this formal evaluation by an external theorem prover (e.g., Lean4, Z3) is recorded permanently as a FormalVerificationReceipt. This receipt anchors the mathematical truth to the ledger, defining success via a definitive boolean is_proved and logging the precise solver evaluation via the satisfiability_state literal (["SATISFIABLE", "UNSATISFIABLE", "UNKNOWN", "OPTIMUM FOUND"]).