In this paper, we show that the lattice of filters of a weakly dicomplemented lattice L can be endowed with a dual weak complementation. Its sublattice of principal filters is shown to be dually isomorphic to the weakly complemented reduct of L. Dense elements and skeletons are revisited. A connection is established between filters of skeletons and certain filters of L.
We propose many-valued logic with internalized meta-judgment (MLIM) and prove its completeness. The syntax of MLIM has a new operator to judge whether the truth value of a formula is a designated value in the original many-valued logic. Using MLIM, designated values are incorporated into its syntax, enabling many-valued logic to be treated as classical logic. The semantics of MLIM is a pair semantics, which determines the validity of formulas by a pair of truth values. The proof theory of MLIM is given as natural deduction obtained by combining the inference rules of classical logic and many-valued logic.
We introduce a novel reduction from the satisfiability problem for a set of propositional signed clauses (Signed SAT) to Mixed Integer Linear Programming (MILP). This reduction provides a scalable and effective approach for solving Signed SAT instances via MILP and can be extended to address a broad class of NP-complete combinatorial decision problems through their reduction to Signed SAT. Furthermore, we present a reduction for a variant of Signed SAT in which each clause is expressed as a disjunction of signed literals rather than as a signed disjunction of literals. Finally, we discuss how these reductions can be adapted for pseudo-Boolean (PB) solving, enabling the use of PB solvers that exploit SAT-based techniques.
This study introduces a human-feasible posture optimization framework that reduces aspiration risk using camera-derived posture information. Joint angles are estimated from sagittal-view images with a body motion link model, aspiration risk is predicted using a machine learning classifier, and posture adjustments are identified through optimization constrained by biomechanical range-of-motion (ROM) limits. In experiments with 68 older adults, constrained optimization reduced predicted aspiration risk by 22.7% while avoiding the anatomically unrealistic postures produced by unconstrained optimization. These findings demonstrate that physiologically grounded constraints are essential for reliable and clinically meaningful posture guidance in aspiration prevention.
The paper presents a discussion of the structure of Haar spectra for ternary bent functions, where the term structure refers to the arrangement of Haar spectral coefficients per packets corresponding to the arrangement of Haar functions used as the kernel of the Haar transform. For a bent function, by considering pairs of 2/3 of Haar coefficients at the same positions in the last two packets in the Haar spectrum, we observe that in the function vector of a bent function, the function values are arranged into triples of adjacent elements of the vector. In construction of bent functions, manipulation the initial bent function over these triples, including re-arrangement of values into new triples, preserve bentness. From each bent function in n variables which has 1/3 zero-valued pairs of Haar coefficients from the last two packets, it can be constructed a set of other bent functions in n variables by referring to the values of bent functions in (n−2) variables.
