Paraconsistent logic

About: Paraconsistent logic is a research topic. Over the lifetime, 1610 publications have been published within this topic receiving 28842 citations.

Quantum Logic as a Fragment of Independence-Friendly Logic

Abstract: The working assumption of this paper is that noncommuting variables are irreducibly interdependent. The logic of such dependence relations is the author's independence-friendly (IF) logic, extended by adding to it sentence-initial contradictory negation ¬ over and above the dual (strong) negation ∼. Then in a Hilbert space ∼ turns out to express orthocomplementation. This can be extended to any logical space, which makes it possible to define the dimension of a logical space. The received Birkhoff and von Neumann “quantum logic” can be interpreted by taking their “disjunction” to be ¬(∼A & ∼B). Their logic can thus be mapped into a Boolean structure to which an additional operator ∼ has been added.

Vagueness-adaptive logic: A pragmatical approach to sorites paradoxes

Abstract: This paper defends a pragmatical approach to vagueness. The vagueness-adaptive logic VAL is a good reconstruction of and an excellent, instrument for human reasoning processes in which vague predicates are involved. Apart from its proof-theory and semantics, a Sorites-treating model based on it is presented, disarming the paradox. The paper opens perspectives with respect to the construction of theories by means of vague predicates.

Analysis of Physical Systems with Paraconsistent Annotated Logic: Introducing the Paraquantum Gamma Factor γ ψ

Abstract: In this paper we use a non-classical logic called ParaQuantum Logic (PQL) which is based on the foundations of the Paraconsistent Annotated logic with annotation of two values (PAL2v). The formalizations of the PQL concepts, which is represented by a lattice with four vertices, leads us to consider Paraquantum logical states ψ which are propagated by means of variations of the evidence Degrees extracted from measurements performed on the Observable Variables of the physical world. In this work we introduce the Paraquantum Gamma Factor γPψ which is an expansion factor on the PQL lattice that act in the physical world and is correlated with the Paraquantum Factor of quantization hψ whose value is associated with a special logical state on the lattice which is identified with the Planck constant h. Our studies show that the behavior of the Paraquantum Gamma Factor γPψ, at the time of reading the evidence Degrees through measurements of the Observable Variables in the physical world, is identical to that one of the Lorentz Factor γ used in the relativity theory. In the final part of this paper we present results about studies of expansion and contraction of the Paraquantum Logical Model which correlate the factors γPψ, and γ. By applying these correlation factors, the lattice of the PQL suitable for the universe understudy can be contracted or expanded, allowing the quantization model to cover the several study fields of physics.

Self-Extensional Three-Valued Paraconsistent Logics

Abstract: A logic $$\mathbf{L}$$ is called self-extensional if it allows to replace occurrences of a formula by occurrences of an $$\mathbf{L}$$ -equivalent one in the context of claims about logical consequence and logical validity. It is known that no three-valued paraconsistent logic which has an implication can be self-extensional. In this paper we show that in contrast, there is exactly one self-extensional three-valued paraconsistent logic in the language of $$\{\lnot ,\wedge ,\vee \}$$ for which $$\vee $$ is a disjunction, and $$\wedge $$ is a conjunction. We also investigate the main properties of this logic, determine the expressive power of its language (in the three-valued context), and provide a cut-free Gentzen-type proof system for it.

Formalizing common sense for scalable inconsistency-robust information integration using Direct Logic(TM) reasoning and the Actor Model

Abstract: Because contemporary large software systems are pervasively inconsistent, it is not safe to reason about them using classical logic. The goal of Direct Logic is to be a minimal fix to classical mathematical logic that meets the requirements of large-scale Internet applications (including sense making for natural language) by addressing the following issues: inconsistency robustness, contrapositive inference bug, and direct argumentation. Direct Logic makes the following contributions over previous work: * Direct Inference (no contrapositive bug for inference) * Direct Argumentation (inference directly expressed) * Inconsistency-robust deduction without artifices such as indices (labels) on propositions or restrictions on reiteration * Intuitive inferences hold including the following: * Boolean Equivalences * Reasoning by splitting for disjunctive cases * Soundness * Inconsistency-robust Proof by Contradiction Since the global state model of computation (first formalized by Turing) is inadequate to the needs of modern large-scale Internet applications the Actor Model was developed to meet this need. Using, the Actor Model, this paper proves that Logic Programming is not computationally universal in that there are computations that cannot be implemented using logical inference. Consequently the Logic Programming paradigm is strictly less general than the Procedural Embedding of Knowledge paradigm.