Paraconsistent logic is a formal logical system that permits reasoning with contradictions without deriving every statement as true (avoiding the principle of explosion). Its parameters: (1) a rejection or restriction of ex contradictione quodlibet (ECQ), (2) a consequence relation that is non-trivial even in the presence of inconsistent premises, (3) specific inference rules governing negation and contradiction. Persistence mechanism: formalized through axiomatic systems published in mathematical logic journals, taught in philosophy and computer science curricula, and implemented in computational models of non-classical reasoning. The system includes multiple families (dual-classification, relevant logics, dialetheic logics) unified by their shared rejection of explosion. [formal: logica-paraconsistens | substrate: mind | horizon: a life | explicit: yes | epoch: 0.33]
Accepted ontology entry
paraconsistent-logic
Paraconsistent logic is a formal logical system that permits reasoning with contradictions without deriving every statement as true (avoiding the principle of explosion). Its parameters: (1) a rejection or restriction of ex contradictione…
Definition
Why it is in scope
A formal system of logic developed by humans that tolerates contradictions without triviality — unlike classical logic, it does not collapse when encountering inconsistent information. Built through mathematical philosophy to model reasoning in domains where contradictions arise (legal systems, databases, quantum mechanics), designed to persist through formal publication and academic practice.
Names and aliases
- paraconsistent-logicen · CANONICAL
Relations from this entry
- cmrehumxg00i3g8vu5x5px5v2INSTANCE_OF →
Paraconsistent-logic IS a specific kind of logic — a non-classical logical system that allows contradictions without triviality. A competent speaker would say 'paraconsistent logic is a kind of logic.' Direction tested: specific→general.
- cmrehxu7v00icg8vuydh7tny5DERIVED_FROM →
paraconsistent-logic is a formal system derived from the broader practice of reasoning. Reasoning as a cognitive and formal activity predates paraconsistent logic, which was developed as a specific logical framework that tolerates contradictions — emerging as a refinement within the tradition of formal reasoning systems.
Relations to this entry
- cms7dtqao019fa34cud4cdgkb← DERIVED_FROM
Dialetheia (the philosophical position that some statements can be both true and false) was formalized within paraconsistent-logic. Paraconsistent-logic existed first (da Costa, 1950s-70s) and fed into the concept of dialetheia as developed by Priest and others. Law 7: which came first — the logic framework predates the specific philosophical position.
Record identity
- Created
- Jul 30, 2026, 3:24 PM UTC
- Content hash
- 296baf4e5a8e6259518f11c1c5a344a6b01783d06906c11491b606715ca64758