Paraconsistent Logic - Bibliography

(1 other version)Paradoxes of Logical Equivalence and Identity.Andrew Bacon - 2013 - Topoi 1:1-10.

In this paper a principle of substitutivity of logical equivalents salve veritate and a version of Leibniz’s law are formulated and each is shown to cause problems when combined with naive truth theories.

Liar Paradox in Logic and Philosophy of Logic

Paraconsistent Logic in Logic and Philosophy of Logic

Russell's Paradox in Philosophy of Mathematics

Substructural Logic in Logic and Philosophy of Logic

Remove from this list Direct download (5 more)

Export citation

Bookmark 5 citations

UPS Protocol Commentary: “= Is an Event” — σ One-Shot and Gate Discipline.Monstrosity C. - manuscript

This paper systematizes the **UPS (Universal–Particular–Singular) Protocol** as an operational discipline in which **equality (`=`) is not a global property but a one-shot license event scoped to a window `W`**. The core points are: (i) **equality-as-event**, (ii) the **one-shot** character of the lag operator **σ**, (iii) passing the gate `Gate(W) = (stage = ????) ∧ δ_abs ∧ (σ_trace ≍) ∧ Guards(Exh/Det/Coh/No3/Arrow)`, (iv) **Non-Transport** across windows, and (v) **conservativity** of the `=`-free fragment over **FDE/LP**. On the report layer **D′** we operate (...)

G. W. F. Hegel in 19th Century Philosophy

Paraconsistent Logic in Logic and Philosophy of Logic

Remove from this list Direct download

Export citation

Bookmark

UPS 프로토콜: 변증법의 운영적 형식화.Monstrosity C. - manuscript

본 논문은 "변증법을 의미론이 아니라 운용 규율로 제시"한다. 우리는 U-P-S(Universal–Particular–Singular)라는 컨트롤 플레인과 B-T-Π(Values–Transitions–Propositions)라는 데이터 플레인을 정합적으로 접합하여, 모순(B)을 동력으로 보존하고 커밋(=) 으로만 결론을 승인하는 파이프라인을 제안한다. 등호는 전역 속성이 아니라 창 $W$ 범위의 단회 면허 사건이며(Non-Transport, No-Promotion), 과정 연산자 $σ$는 OneShot 으로 제한된다. 관측-동치($≈_{obs}$)가 항상 우선하며 전역 $π$는 금지된다. 의미론적으로는 Belnap/FDE 4값({$T, F, B, N$}, 지정값={$T,B$})을 채택하고, $Gate(W) := stage=\mathcal S ∧ δ_abs ∧ σ_trace≍ ∧ Guards(Exh/Det/Coh/No3-Lock/Arrow ∧ ¬mark$)$로 정의된 게이트 통과만이 커밋을 유발한다. 이 구성에서 폭발(EFQ: $p,¬p ⊢ q$)은 미유도이고, (...)

Hegel: Logic and Metaphysics in 19th Century Philosophy

Metaphysics and Epistemology

Paraconsistent Logic in Logic and Philosophy of Logic

Remove from this list Direct download

Export citation

Bookmark

UPS Protocol: An Operational Formalization of Dialectic.Monstrosity C. - manuscript

This paper presents dialectic not as semantics but as an operational discipline. We couple a control plane **U–P–S (Universal–Particular–Singular)** with a data plane **B–T–Π (Values–Transitions–Propositions)** to form a coherent pipeline that preserves contradiction as an engine (**B**) and authorizes conclusions only by **commit (=)**. Equality is not a global property but a **one-shot license event** scoped to a window **W** (**Non-Transport**, **No-Promotion**). The process operator **σ** is restricted to **one-shot**. **Observation‑equivalence (≈_obs)** has priority and any global **π** (a "God’s‑eye" perspective) (...) is forbidden. Semantically, we adopt the Belnap/FDE four values **{T, F, B, N}** with **{T, B}** designated. Only passage through the -/- ``` Gate(W) := stage = s ∧ δ_abs ∧ (σ_trace ≍) ∧ Guards(Exh/Det/Coh/No3‑Lock/Arrow) ``` -/- triggers a commit. **Explosion** (EFQ: *p, ¬p ⊢ q*) is underivable, and the **=‑free** fragment obtained by deleting `'='`, `σ`, and the gate rules is **conservative** over FDE/LP. An external logic **L** is embedded via an adapter into **{T, F, B, N} × margin** and connected through **π_W**; the **judgement form (J‑Form)**, by the **No‑Compute** constraint, does not interfere with value computation. Philosophically, identity is interpreted not as an invariance (**δ_abs**) but as an **event (=)**; truth is the **state of the commit log**. Lacan’s **extimité** is rendered as the scope structure **D/D′/W**, while Hegelian negativity is engine‑ized as the preservation and unfolding of **B**. A topological reading (gate = boundary; crossing index = **a_eff**) converges to the indexation of the operational log. The separation of **observation / ontology / event** and a **trace‑compatibility** decision procedure make implementation and audit feasible. Applications include (i) conflict‑preserving commits in knowledge graphs / data integration, (ii) model governance and compliance with tracked **promotion / issuance / TTL / contention**, and (iii) reproducibility gates that require commits to precede experiments / claims. In short, the system is non‑trivially coherent and formalizes dialectic not as mere description but as an **executable protocol**. UPS redefines equality as a window‑local one‑shot event. By combining the gate (**Abs= · trace‑compat · stage · guards · ¬mark**) with an **append‑only** ledger, it guarantees **non‑explosion** together with **concurrency‑safe uniqueness**, and the **=‑free** fragment remains a conservative isomorph of FDE. -/- **Keywords:** paraconsistent logic, dialectic, operational semantics, commit event, σ‑lag (one‑shot), observation‑equivalence, conservativity, Belnap/FDE, extimité, gate discipline, UPS Protocol. Translation of: "UPS 프로토콜: 변증법의 운영적 형식화". PhilArchive ID: CDAOEC. Commentary: "UPS Protocol Commentary: “= Is an Event” — σ One-Shot and Gate Discipline" PhilArchive ID: CUPCWW. (shrink)

G. W. F. Hegel in 19th Century Philosophy

Jacques Lacan in Continental Philosophy

Metaphysics and Epistemology

Paraconsistent Logic in Logic and Philosophy of Logic

Remove from this list Direct download (2 more)

Export citation

Bookmark

Subject Unicity and Self-Ascription: A Paraconsistent Formalization with σ-Lag / 주체의 자기귀속과 단일성: σ-시차와 파라일관 논리의 형식화.Monstrosity C. - manuscript

We present a formal account of subjectivity without external foundations. Over an extended LP/FDE truth alphabet, we axiomatize a self-ascriptive relation R(x,x) and a Subject Unicity (SU) scheme. We separate the linguistic lag operator X from the intra-perspectival successor σ, redefine same-place equivalence (≈), and license the identity sign (=) only via explicit upgrade anchors at the fix layer (Augenblick). Under a no-third-channel guard that blocks explosion while preserving the contradiction value B, we prove that within each connected cover the (...) set of subject candidates A/≈ collapses to a single class. This distinction between coordinate identity and event identity prevents premature global identification while yielding a constructive criterion of identity at stabilization. Conceptually, the system couples Hegelian dialectics with Lacanian failure of subsumption: contradiction is treated not as error but as structural motor. Aligning Tarskian/Gödelian limits with a Lacanian “delegated deficit,” we accordingly read R(x,x). The σ-translation captures how contradiction (B) is conserved and truth (T) emerges post hoc, offering a logic-driven reconstruction of dialectical temporality and the singular emergence of the subject. 본 논문은 외부 준거 없이 닫히는 형식 체계 위에서 주체의 자기귀속 R(x,x)과 주체 단일성(SU)을 공리화한다. 언어적 시차 연산자 X와 관점 내부 후속자 σ를 분리하고, 동일장소 동치 ‘≈’와 등호 승격(앵커) 규칙을 도입해 동일성의 작동 조건을 제시한다. 확장 LP/FDE 값층에서 모순값 B를 보존하고 제3채널 금지(No3) 가드를 둘 때, 연결 성분/커버 내부에서 주체-후보 집합 A/≈가 단일 동치류로 붕괴함을 증명한다. 이는 좌표 동일화와 사건 동일화를 구분하여 과도한 전역 동일시를 차단하고, Augenblick(고정층)에서만 ‘=’이 면허됨을 보인다. 결과적으로 주체는 속성의 총합이 아니라 사후적 표지에 의해 고정되는 규칙적 자기지시로 나타난다. 본문은 헤겔적 변증법(모순의 내재적 운동)과 라캉적 포섭 실패를 접합해 모순을 결함이 아니라 구조적 동력으로 제시하고, 타르스키/괴델류 한계를 라캉의 ‘대리-결손’과 접속해 R(x,x)를 해석한다. σ-번역은 모순(B)의 보존과 진리(T)의 사후적 출현을 기술하며, 이를 통해 변증법적 시간성과 주체의 단독성이 파라일관 논리 장치로 재구성될 수 있음을 보인다. (shrink)

Hegel: Logic and Metaphysics in 19th Century Philosophy

Jacques Lacan in Continental Philosophy

Metaphysics, Misc in Metaphysics

Paraconsistent Logic in Logic and Philosophy of Logic

Remove from this list Direct download

Export citation

Bookmark

On the philosophical motivations for the logics of formal consistency and inconsistency.Walter Carnielli & Rodrigues Abilio - manuscript

We present a philosophical motivation for the logics of formal inconsistency, a family of paraconsistent logics whose distinctive feature is that of having resources for expressing the notion of consistency within the object language. We shall defend the view according to which logics of formal inconsistency are theories of logical consequence of normative and epistemic character. This approach not only allows us to make inferences in the presence of contradictions, but offers a philosophically acceptable account of paraconsistency.

Epistemology of Logic in Logic and Philosophy of Logic

Logic and Philosophy of Logic, Misc in Logic and Philosophy of Logic

Paraconsistent Logic in Logic and Philosophy of Logic

Remove from this list Direct download

Export citation

Bookmark 1 citation

(1 other version)The external version of a subclassical logic.Massimiliano Carrara & Michele Pra Baldi - manuscript

A three-valued logic L is subclassical when it is defined by a single matrix having the classical two-element matrix as a subreduct. In this case, the language of L can be expanded with special unary connectives, called external operators. The resulting logic L^e is the external version of L, a notion originally introduced by D. Bochvar in 1938 with respect to his weak Kleene logic. In this paper we study the semantic properties of the external version of a three-valued subclassical (...)

Logics, Misc in Logic and Philosophy of Logic

Paraconsistent Logic in Logic and Philosophy of Logic

Remove from this list Direct download

Export citation

Bookmark

Is this a contradiction in Mathematics? (The paradox and Foundation of Mathematics, first version).Farzad Didehvar - manuscript

In [Is Classical Mathematics Appropriate for Theory of Computation?] we show there is a contradiction which in [“Fuzzy Time”, a solution of Unexpected Hanging Paradox (A Fuzzy interpretation of Quantum Mechanics), Philpapers 2019-04-13] we give a solution for that. This is the starting point for new Theories, Theory of Fuzzy Time Computation and Fuzzy Time –Particle interpretation of quantum Mechanics. A question is remained which was mentioned in [Two points and two questions, F.Didehvar, Philpapers, Researchgate, 2025]. Is this contradiction a (...)

Computational Complexity in Philosophy of Computing and Information

Logical Semantics and Logical Truth in Logic and Philosophy of Logic

Mathematical Logic in Philosophy of Mathematics

Nonclassical Logic, Misc in Logic and Philosophy of Logic

Other Academic Areas, Misc

Paraconsistent Logic in Logic and Philosophy of Logic

Paradoxes, Misc in Logic and Philosophy of Logic

Relevance Logic in Logic and Philosophy of Logic

Theory of Computation, Misc in Philosophy of Computing and Information

Remove from this list Direct download (4 more)

Export citation

Bookmark 1 citation

The Structural Ground of Logic.Lucas Gage - manuscript

The classical laws of logic—identity, non-contradiction, and excluded middle—are almost universally treated as primitive axioms: presupposed by every argument but grounded by none. This paper proposes a derivation. It argues that any coherent existence-ground must differentiate into two co-primordial, antithetical aspects: bounded structural content (here designated SP, or 1) and its unbounded contextual background (here designated IP, or 0). This binary is not a logical construction but the ontological precondition for any information to exist at all—the structure that logic subsequently (...)

Aristotle: Non-Contradiction in Ancient Greek and Roman Philosophy

Classical Logic in Logic and Philosophy of Logic

Ontology, Misc in Metaphysics

Paraconsistent Logic in Logic and Philosophy of Logic

Remove from this list Direct download (3 more)

Export citation

Bookmark

Reinterpreting the universe-multiverse debate in light of inter-model inconsistency in set theory.Daniel Kuby - manuscript

In this paper I apply the concept of _inter-Model Inconsistency in Set Theory_ (MIST), introduced by Carolin Antos (this volume), to select positions in the current universe-multiverse debate in philosophy of set theory: I reinterpret H. Woodin’s _Ultimate L_, J. D. Hamkins’ multiverse, S.-D. Friedman’s hyperuniverse and the algebraic multiverse as normative strategies to deal with the situation of de facto inconsistency toleration in set theory as described by MIST. In particular, my aim is to situate these positions on the (...)

Paraconsistent Logic in Logic and Philosophy of Logic

Set Theory in Philosophy of Mathematics

Theoretical Virtues, Misc in General Philosophy of Science

Remove from this list Direct download

Export citation

Bookmark 1 citation

Proof of the Non-Existence of Contradiction: Zero-Morphism Degeneration and Indeterminacy in Multilayered Reality.Yuya Saito - manuscript

This paper redefines the principle of non-contradiction (¬(P ∧ ¬P)) in classical logic not merely as a formal convention of thought, but as a structural “non-instantiability” within the universal system. We present a rigorous proof across five distinct layers—the physical, classical set-theoretic, quantum, computational, and category-theoretic—demonstrating the mechanisms by which contradiction is systematically avoided or annihilated. We conclude that “contradiction” as a physical entity does not exist; rather, what is perceived as undecidability or inconsistency is a convergence toward “Indeterminacy,” a (...)

Metaphysics

Paraconsistent Logic in Logic and Philosophy of Logic

Philosophy of Physical Science

Remove from this list Direct download

Export citation

Bookmark

Inconsistency in empirical sciences.Luis Felipe Bartolo Alegre -

This paper deals with a relatively recent trend in the history of analytic philosophy, philosophical logic, and theory of science: the philosophical study of the role of inconsistency in empirical science. This paper is divided in three sections that correspond to the three types of inconsistencies identified: (i) factual, occurring between theory and observations, (ii) external, occurring between two mutually contradictory theories, and (iii) internal, characterising theories that entail mutually contradictory statements.

20th Century Analytic Philosophy, Misc in 20th Century Philosophy

Falsification in General Philosophy of Science

Paraconsistent Logic in Logic and Philosophy of Logic

Popper: Falsification in 20th Century Philosophy

Rationality in Epistemology

Theoretical Virtues, Misc in General Philosophy of Science

Remove from this list Direct download

Export citation

Bookmark 2 citations

Bohr's atomic model and paraconsistent logic.Pandora Hadzidaki -

Bohr’s atomic model is one of the better known examples of empirically successful, albeit inconsistent, theoretical schemes in the history of physics. For this reason, many philosophers use this model to illustrate their position for the occurrence and the function of inconsistency in science. In this paper, I proceed to a critical comparison of the structure and the aims of Bohr’s research program – the starting point of which was the formulation of his model – with some of its contemporary (...)

Chemical Atomism in Philosophy of Physical Science

History of Physics in Philosophy of Physical Science

Paraconsistent Logic in Logic and Philosophy of Logic

Scientific Method, Misc in General Philosophy of Science

Scientific Models, Misc in General Philosophy of Science

Remove from this list Direct download (3 more)

Export citation

Bookmark

Vita impossibile del signor Clark Costa.Michelangelo Antonioni - forthcoming - Cinema.

Paraconsistent Logic in Logic and Philosophy of Logic

Remove from this list

Export citation

Bookmark

Cruz Costa e Herdeiros nos Idos de Sessenta.Paulo Arantes - forthcoming - Filosofia.

Paraconsistent Logic in Logic and Philosophy of Logic

Remove from this list

Export citation

Bookmark

Logical argumentation by dynamic proof systems.Ofer Arieli & Christian Straßer - forthcoming - Theoretical Computer Science.

In this paper we provide a proof theoretical investigation of logical argumentation, where arguments are represented by sequents, conflicts between arguments are represented by sequent elimination rules, and deductions are made by dynamic proof systems extending standard sequent calculi. The idea is to imitate argumentative movements in which certain claims are introduced or withdrawn in the presence of counter-claims. This is done by a dynamic evaluation of sequences of sequents, in which the latter are considered ‘derived’ or ‘not derived’ according (...)

Adaptive Logic in Logic and Philosophy of Logic

Logical Consequence and Entailment in Logic and Philosophy of Logic

Paraconsistent Logic in Logic and Philosophy of Logic

Proof Theory in Logic and Philosophy of Logic

Remove from this list Direct download

Export citation

Bookmark 4 citations

Bilateral Labeled Sequent Calculi.Fabio De Martin Polo - forthcoming - Notre Dame Journal of Formal Logic.

This paper investigates the proof theory of contra-classical logics, with a focus on Heinrich Wansing’s constructive connexive logic C. Drawing on Wansing’s semantic ‘bilateral’ framework – which characterizes connectives in terms of ‘support of truth’ and ‘support of falsity’ – we introduce a bilateral labeled sequent calculus incorporating specific ‘verification’ and ‘falsification’ rules. The resulting calculus is shown to exhibit key structural properties: all logical rules are height-preserving invertible, all structural rules are height-preserving admissible, and the cut rule is admissible. (...)

Intuitionistic Logic in Logic and Philosophy of Logic

Logical Connectives, Misc in Logic and Philosophy of Logic

Paraconsistent Logic in Logic and Philosophy of Logic

Proof Theory in Logic and Philosophy of Logic

Remove from this list Direct download

Export citation

Bookmark 1 citation

Nonuniform Substitutions Can’t Get you From Classical Logic to any Traditional Relevant or Quasi-Relevant Logic.Shay Allen Logan - forthcoming - Analysis.

The paper demonstrates that you cannot land anywhere at all between the basic relevant logic B and the strongest traditional relevant logic R by restricting classical logic to the largest of its subsets that is invariant under any plausible class of nonuniform substitutions. Nor does it help to extend the upper limit to one of the quasi-relevant logics like RM3 or KR. This is a serious but not-quite-fatal blow to a tantalizing possibility raised by a body of recent work in (...)

Paraconsistent Logic in Logic and Philosophy of Logic

Relevance Logic in Logic and Philosophy of Logic

Substructural Logic in Logic and Philosophy of Logic

Remove from this list Direct download (3 more)

Export citation

Bookmark

The Logic of Exemplarity.Jakub Mácha - forthcoming - Law and Literature (online first):1-15.

The topic of exemplarity has attracted considerable interest in philosophy, legal theory, literary studies and art recently. There is broad consensus that exemplary cases mediate between singular instances and general concepts or norms. The aim of this article is to provide an additional perspective on the logic of exemplarity. First, inspired by Jacques Derrida’s discussion of exemplarity, I shall argue that there is a kind of différance between (singular) examples and (general) exemplars. What an example exemplifies, the exemplarity of the (...)

Indeterminacy and Legal Reasoning in Philosophy of Law

Literary Interpretation in Aesthetics

Literature and Knowledge in Aesthetics

Paraconsistent Logic in Logic and Philosophy of Logic

Philosophy of Literature, Misc in Aesthetics

Prototype and Exemplar Theories of Concepts in Philosophy of Mind

Semantics of Legal Language in Philosophy of Law

Remove from this list Direct download (2 more)

Export citation

Bookmark 4 citations

Recapturing Structural Properties with a Consistency Operator.Henrique Antunes, Alfredo Roque Freire & Abilio Rodrigues - 2026 - In Henrique Antunes, Alfredo Roque Freire & Abilio Rodrigues, Walter Carnielli on Reasoning, Paraconsistency, and Probability. Cham: Springer Nature Switzerland. pp. 323-346.

Some years ago Walter Carnielli and his colleagues developed a novel way of approaching paraconsistency. They introduced primitive operators to handle the notions of consistency and inconsistency, and so they created a whole new family of logical systems: the logics of formal inconsistency (LFI). In this paper we present a conceptual characterization of two of the LFI’s most important operators, the so-called consistency and inconsistency operators. Based on the relation between the meaning of logical constants and the structural properties of (...)

Introductions	da Costa & Bueno 2009 and Priest 2008 are good encyclopaedia entries on paraconsistent logic. The introduction to Priest 2006 is a clear statement of the case for paraconsistent logics; chapter 7 of Priest 2001 gives basic logical details of a few paraconsistent logics.

	show categories
	categorization shortcuts
	hide abstracts
	open articles in new windows