Adding Involution to Residuated Structures

Two constructions for adding an involution operator to residuated ordered monoids are investigated. One preserves integrality and the mingle axiom x ²x but fails to preserve the contraction property xx ². The other has the opposite preservation properties. Both constructions preserve commutativity as well as existent nonempty meets and joins and self-dual order properties. Used in conjunction with either construction, a result of R.T. Brady can be seen to show that the equational theory of commutative distributive residuated lattices (without involution) is decidable, settling a question implicitly posed by P. Jipsen and C. Tsinakis. The corresponding logical result is the (theorem-) decidability of the negation-free axioms and rules of the logic RW, formulated with fusion and the Ackermann constant t. This completes a result of S. Giambrone whose proof relied on the absence of t.     

A non-finitely based quasi-variety of De Morgan algebras

In this paper we exhibit a non-finitely based, finitely generated quasi-variety of De Morgan algebras and determine the bottom of the lattices of sub-quasi-varieties of Kleene and De Morgan algebras.Supported by Vicerrectoría Académica de la Facultad de Ciencias and by División de Investigación, Sede Bogotá of the Universidad Nacional de Colombia.Special issue of Studia Logica: Algebraic Theory of Quasivarieties Presented by M. E. Adams, K. V. Adaricheva, W. Dziobiak, and A. V. Kravchenko     

On a Contraction-Less Intuitionistic Propositional Logic with Conjunction and Fusion

In this paper we prove the equivalence between the Gentzen system G _LJ*\c , obtained by deleting the contraction rule from the sequent calculus LJ* (which is a redundant version of LJ), the deductive system IPC*\c and the equational system associated with the variety RL of residuated lattices. This means that the variety RL is the equivalent algebraic semantics for both systems G _LJ*\c in the sense of [18] and [4], respectively. The equivalence between G _LJ*\c and IPC*\c is a strengthening of a result obtained by H. Ono and Y. Komori [14, Corollary 2.8.1] and the equivalence between G _LJ*\c and the equational system associated with the variety RL of residuated lattices is a strengthening of a result obtained by P.M. Idziak [13, Theorem 1].An axiomatization of the restriction of IPC*\c to the formulas whose main connective is the implication connective is obtained by using an interpretation of G _LJ*\c in IPC*\c.     

New understanding of the role of coincidence site lattice boundaries in abnormal grain growth of aluminium alloy

The sequential microstructure evolution of abnormal grain growth (AGG) in the aluminium alloy (AA5052) was investigated to analyse the migration behaviour of coincidence site lattice (CSL) boundaries, which are known to play an important role in inducing AGG. The sequential evolution showed that CSL boundaries tend to disappear more slowly than general boundaries at the growth front of abnormally growing grains. Especially, the migration rate of Σ9 boundaries was noticeably low, which is contrary to the previous suggestions.     

Quantized intrinsically localized modes of a 3D lattice

Intrinsically Localized Modes are anharmonic oscillations found in one-dimensional systems, and occur relatively infrequently in classical higher dimensional lattices. However, when ILMs appear in simulations of classical lattices, their energies are too high for them to be seen in thermal equilibrium. We investigate quantized ILMs in a three-dimensional lattice using the Ladder Approximation, and find that ILMs occur preferentially for centre of mass momenta at which the van-Hove singularities in the two-phonon density of states coalesce. For interactions larger than a critical value, the ILMs form above the top of the two-phonon continuum, but fall into the continuum as q? is shifted away from the optimal value. This indicates that ILM excitations may be more ubiquitous in 3D lattices than previously expected. Furthermore, we find that the ILMs have intrinsic spins of either S = 0 or S = 2 and have internal structures associated with their spatial symmetry.     

Fuzzy system for intelligent word recognition using a regular grammar

We present a new approach for off-line intelligent word recognition based on a fuzzy classification model. First, we segment a word into its single characters, and label each pixel as vertical or as horizontal so that we can group all the pixels into vertical or horizontal strokes. Then, we use dynamic zoning to obtain the locations of the connections between the vertical strokes – which are the main strokes – and the horizontal ones. These features let us construct the representative string of a character using a regular grammar and, subsequently, use a Deterministic Finite Automaton to check them out. To accomplish the recognition, we use a Fuzzy Lattice Reasoning classifier. The combination of the representative strings and the fuzzy classifier provides promising performance rates.     

The complexity of satisfiability for fragments of hybrid logic—Part I

The satisfiability problem of hybrid logics with the downarrow binder is known to be undecidable. This initiated a research program on decidable and tractable fragments.In this paper, we investigate the effect of restricting the propositional part of the language on decidability and on the complexity of the satisfiability problem over arbitrary, transitive, total frames, and frames based on equivalence relations. We also consider different sets of modal and hybrid operators. We trace the border of decidability and give the precise complexity of most fragments, in particular for all fragments including negation. For the monotone fragments, we are able to distinguish the easy from the hard cases, depending on the allowed set of operators.     

Constructive Logic with Strong Negation is a Substructural Logic. II

The goal of this two-part series of papers is to show that constructive logic with strong negation N is definitionally equivalent to a certain axiomatic extension NFL _ew of the substructural logic FL _ew . The main result of Part I of this series [41] shows that the equivalent variety semantics of N (namely, the variety of Nelson algebras) and the equivalent variety semantics of NFL _ew (namely, a certain variety of FL _ew -algebras) are term equivalent. In this paper, the term equivalence result of Part I [41] is lifted to the setting of deductive systems to establish the definitional equivalence of the logics N and NFL _ew . It follows from the definitional equivalence of these systems that constructive logic with strong negation is a substructural logic. Presented by Heinrich Wansing     

Semisimplicity,EDPC and Discriminator Varieties of Residuated Lattices

We prove that all semisimple varieties of FL _ew-algebras are discriminator varieties. A characterisation of discriminator and EDPC varieties of FL _ew-algebras follows. It matches exactly a natural classification of logics over FL _ew proposed by H. Ono.     

From Semirings to Residuated Kleene Lattices

We consider various classes of algebras obtained by expanding idempotent semirings with meet, residuals and Kleene-*. An investigation of congruence properties (e-permutability, e-regularity, congruence distributivity) is followed by a section on algebraic Gentzen systems for proving inequalities in idempotent semirings, in residuated lattices, and in (residuated) Kleene lattices (with cut). Finally we define (one-sorted) residuated Kleene lattices with tests to complement two-sorted Kleene algebras with tests.