Lattice Logic,Bilattice Logic and Paraconsistent Quantum Logic: a Unified Framework Based on Monosequent Systems

Journal of Philosophical Logic - Lattice logic, bilattice logic, and paraconsistent quantum logic are investigated based on monosequent systems. Paraconsistent quantum logic is an extension of...     

Quantized Linear Logic,Involutive Quantales and Strong Negation

A new logic, quantized intuitionistic linear logic (QILL), is introduced, and is closely related to the logic which corresponds to Mulvey and Pelletier's (commutative) involutive quantales. Some cut-free sequent calculi with a new property quantization principle and some complete semantics such as an involutive quantale model and a quantale model are obtained for QILL. The relationship between QILL and Wansing's extended intuitionistic linear logic with strong negation is also observed using such syntactical and semantical frameworks.     

Proof Theory of Paraconsistent Quantum Logic

Paraconsistent quantum logic, a hybrid of minimal quantum logic and paraconsistent four-valued logic, is introduced as Gentzen-type sequent calculi, and the cut-elimination theorems for these calculi are proved. This logic is shown to be decidable through the use of these calculi. A first-order extension of this logic is also shown to be decidable. The relationship between minimal quantum logic and paraconsistent four-valued logic is clarified, and a survey of existing Gentzen-type sequent calculi for these logics and their close relatives is addressed.     

Falsification-Aware Semantics and Sequent Calculi for Classical Logic

Journal of Philosophical Logic - In this study, falsification-aware semantics and sequent calculi for first-order classical logic are introduced and investigated. These semantics and sequent...     

Proof Systems Combining Classical and Paraconsistent Negations

New propositional and first-order paraconsistent logics (called L _ω and FL _ω , respectively) are introduced as Gentzen-type sequent calculi with classical and paraconsistent negations. The embedding theorems of L _ω and FL _ω into propositional (first-order, respectively) classical logic are shown, and the completeness theorems with respect to simple semantics for L _ω and FL _ω are proved. The cut-elimination theorems for L _ω and FL _ω are shown using both syntactical ways via the embedding theorems and semantical ways via the completeness theorems. Presented by Yaroslav Shramko and Heinrich Wansing     

Substructural Implicational Logics Including the Relevant Logic E

We introduce several restricted versions of the structural rules in the implicational fragment of Gentzen's sequent calculus LJ. For example, we permit the applications of a structural rule only if its principal formula is an implication. We investigate cut-eliminability and theorem-equivalence among various combinations of them. The results include new cut-elimination theorems for the implicational fragments of the following logics: relevant logic E, strict implication S4, and their neighbors (e.g., E-W and S4-W); BCI-logic, BCK-logic, relevant logic R, and the intuitionistic logic. This revised version was published online in June 2006 with corrections to the Cover Date.     

Embedding Friendly First-Order Paradefinite and Connexive Logics

Journal of Philosophical Logic - First-order intuitionistic and classical Nelson–Wansing and Arieli–Avron–Zamansky logics, which are regarded as paradefinite and connexive logics,...     

Elusive piety: Hajj logistics and local politics in Tatarstan,Dagestan and the Crimea

ABSTRACT

This article explores a barely addressed but crucial element of Muslim politics in contemporary Russia: hajj logistics and its repercussions in Muslim communities. Focusing on Tatarstan, Dagestan and the annexed Crimea, I first introduce the actors orchestrating the Russian hajj, encompassing coordination with the Muslim Spiritual Boards and tour companies, transportation, medical care and distribution of the hajj quota annually provided by Saudi Arabia. I then illustrate the politics of quota distribution and the dynamics of the hajj market. While Islamic leaders definitely need the state’s increasing support and mediation, central and regional administrations also attempt to demarcate their own sphere of commitment to Muslim citizens’ sacred journey, often invoking the separation of state and religion. Nonetheless it is Muslim citizens searching for the optimal price and service for the holiest journey who shape Russia’s hajj market and the politics of the quota across Tatarstan, Dagestan and the Crimea.     

A Hierarchy of Weak Double Negations

In this paper, a way of constructing many-valued paraconsistent logics with weak double negation axioms is proposed. A hierarchy of weak double negation axioms is addressed in this way. The many-valued paraconsistent logics constructed are defined as Gentzen-type sequent calculi. The completeness and cut-elimination theorems for these logics are proved in a uniform way. The logics constructed are also shown to be decidable.     

Synchronized Linear-Time Temporal Logic

A new combined temporal logic called synchronized linear-time temporal logic (SLTL) is introduced as a Gentzen-type sequent calculus. SLTL can represent the n-Cartesian product of the set of natural numbers. The cut-elimination and completeness theorems for SLTL are proved. Moreover, a display sequent calculus ??SLTL is defined.