Mathematical Logic Quarterly最新文献

In this paper, we propose the strong* proximity lattices, and prove that the categories $�\mathrm{QFS}$ and $��S^{*}�\mathrm{PL}�$ are categorically equivalent, building on the framework established by Achim Jung and Philipp Sünderhauf. $�\mathrm{QFS}$ denotes the category of all QFS-domains and continuous functions. $��S^{*}�\mathrm{PL}�$ denotes the category of the strong* proximity lattices with the approximable relations. This answers the question posed by Achim Jung at the conference ISDT'13.

This article introduces a novel definition of $��(�k�,�s�)�$-Hilfer fractional derivative. Based on this derivative, some fractional Wirtinger type inequalities are established for the $�L_p$ spaces, where $��p�>�1�$ by using Hölder's inequality. Various related special cases are also presented. To validate our main results, examples with graphical representations are provided. Applications of $��(�k�,�s�)�$-Hilfer fractional Wirtinger-type inequalities are demonstrated in terms of arithmetic mean and geometric mean-type inequality.

We introduce an $�\omega$-ary operation on the class of the ordinals, which is strictly monotone in all significant cases. We provide order-theoretical characterizations as the rank of a sequence in a well-founded order and as a mixed sum of the ordinals in the sequence.

We introduce the concept of right-continuous mappings from [0,1) to the power set of finite elements in a complete semilattice and define a closure operator on the set $�P_r$ of right-continuous mappings. We show that the lattice of fuzzy ideals on the semilattice of finite elements is isomorphic to the lattice of closed elements concerning the closure operator. Furthermore, we give equivalent conditions for regular closure operators on the set of right-continuous mappings to be quasi-algebraic. Finally, we prove the lattice of fuzzy ideals on the set of finite elements in an algebraic semilattice is subdirectly embedded into the product of copies of the semilattice, and show the subdirect embedding has a universal mapping property.

In this study, the Minkowski and Fejér-Hermite-Hadamard (H-H) type inequalities are generalized by utilizing the modified Atangana-Baleanu (A-B) fractional operators. These fractional operators, defined by their nonlocal and nonsingular kernels provide a new way to generalize these classical inequalities. The inequalities are verified through several illustrative examples and corresponding graphs. A new application involving the digamma function is presented to demonstrate the significance of the results. This research opens new avenues for establishing further inequalities via fractional operators.

Automated deduction based on contradiction separation extends the binary resolution principle, offering a novel approach to deductive inference rules. Constructing standard contradictions is essential for its efficiency. This paper systematically investigates two new types of standard contradictions in propositional and first-order logic, enriching the library of standard contradictions and enhancing its effectiveness. First, we define two types of standard contradictions: sign-boundary contradictions and diagonal vacancy-type contradictions. Next, we propose the corresponding construction methods and present their properties related to contradiction composition and literal addition. Furthermore, we explore the transformations between these two types of contradictions and analyze the conditions necessary to construct standard contradictions. Finally, we extend these findings to first-order logic, demonstrating their applicability in more complex logical systems.

In this study, we extend the additively generated triangular norms from the framework of the unit interval to that of partially ordered sets. We present several conditions under which this formula $��\psi �T�(�\phi �x�,�\phi �y�)�$ yields a t-norm, where $��P�,�Q�$ are partially ordered sets, $��\phi �:�P�\to �Q�$ and $��\psi �:�Q�\to �P�$ are monotone functions and $�T$ is a t-norm/t-conorm on $�Q$. The partially ordered semigroups induced by $��\psi �T�(�\phi �x�,�\phi �y�)�$ are order-preserving/order-reversing homomorphic to semigroup deformations of the semigroup induced by $�T$.