Big lattices of hereditary and natural classes of linear modular lattices

2021 ◽  
Vol 82 (4) ◽  
Author(s):  
Sebastián Pardo-Guerra ◽  
Hugo A. Rincón-Mejia ◽  
Manuel G. Zorrilla-Noriega
Keyword(s):  
Modular Lattices ◽  
Natural Classes

scholarly journals More on Modal Aspects of Default Logic1

1992 ◽  
Vol 17 (1-2) ◽  
pp. 99-116
Author(s):  
V. Wiktor Marek ◽  
Miroslaw Truszczynski
Keyword(s):  
Modal Logic ◽  
Default Logic ◽  
Nonmonotonic Logic ◽  
Default Reasoning ◽  
Default Theory ◽  
Autoepistemic Logic ◽  
The Relationship ◽  
Natural Classes ◽  
Weak Extension

Investigations of default logic have been so far mostly concerned with the notion of an extension of a default theory. It turns out, however, that default logic is much richer. Namely, there are other natural classes of objects that might be associated with default reasoning. We study two such classes of objects with emphasis on their relations with modal nonmonotonic formalisms. First, we introduce the concept of a weak extension and study its properties. It has long been suspected that there are close connections between default and autoepistemic logics. The notion of weak extension allows us to precisely describe the relationship between these two formalisms. In particular, we show that default logic with weak extensions is essentially equivalent to autoepistemic logic, that is, nonmonotonic logic KD45. In the paper we also study the notion of a set of formulas closed under a default theory. These objects are shown to correspond to stable theories and to modal logic S5. In particular, we show that skeptical reasoning with sets closed under default theories is closely related with provability in S5. As an application of our results we determine the complexity of reasoning with weak extensions and sets closed under default theories.

scholarly journals Seven-modular lattices and a septic base Jacobi identity

2003 ◽  
Vol 99 (2) ◽  
pp. 361-372 ◽  
Author(s):  
Heng Huat Chan ◽  
Kok Seng Chua ◽  
Patrick Solé
Keyword(s):  
Jacobi Identity ◽  
Modular Lattices

Matchings and Radon transforms in lattices II. Concordant sets

1987 ◽  
Vol 101 (2) ◽  
pp. 221-231 ◽  
Author(s):  
Joseph P. S. Kung
Keyword(s):  
Incidence Matrix ◽  
Finite Lattice ◽  
Möbius Function ◽  
Radon Transforms ◽  
Modular Lattices ◽  
Covering Theorem ◽  
Mobius Function ◽  
Finite Lattices ◽  
Semimodular Lattices

AbstractLet and ℳ be subsets of a finite lattice L. is said to be concordant with ℳ if, for every element x in L, either x is in ℳ or there exists an element x+ such that (CS1) the Möbius function μ(x, x+) ≠ 0 and (CS2) for every element j in , x ∨ j ≠ x+. We prove that if is concordant with ℳ, then the incidence matrix I(ℳ | ) has maximum possible rank ||, and hence there exists an injection σ: → ℳ such that σ(j) ≥ j for all j in . Using this, we derive several rank and covering inequalities in finite lattices. Among the results are generalizations of the Dowling-Wilson inequalities and Dilworth's covering theorem to semimodular lattices, and a refinement of Dilworth's covering theorem for modular lattices.

UNDECIDABILITY OF THE THEORIES OF CLASSES OF STRUCTURES

2014 ◽  
Vol 79 (4) ◽  
pp. 1001-1019 ◽  
Author(s):  
ASHER M. KACH ◽  
ANTONIO MONTALBÁN
Keyword(s):  
Direct Product ◽  
Disjoint Union ◽  
Second Order ◽  
Linear Orders ◽  
Second Order Arithmetic ◽  
Order Arithmetic ◽  
Natural Classes ◽  
Product Of Groups

AbstractMany classes of structures have natural functions and relations on them: concatenation of linear orders, direct product of groups, disjoint union of equivalence structures, and so on. Here, we study the (un)decidability of the theory of several natural classes of structures with appropriate functions and relations. For some of these classes of structures, the resulting theory is decidable; for some of these classes of structures, the resulting theory is bi-interpretable with second-order arithmetic.

scholarly journals Baer-Galois connections and applications

2014 ◽  
Vol 30 (2) ◽  
pp. 225-229
Author(s):  
GABRIELA OLTEANU ◽  
Keyword(s):  
Modular Lattices ◽  
Galois Connections ◽  
Baer Modules

We define Baer-Galois connections between bounded modular lattices. We relate them to lifting lattices and we show that they unify the theories of (relatively) Baer and dual Baer modules.

scholarly journals The blind choreographer: evolution of social norms and correlated equilibria

2018 ◽  
Author(s):  
Bryce Morsky ◽  
Erol Akçay
Keyword(s):  
Social Norms ◽  
Social Life ◽  
Evolutionary Dynamics ◽  
Population Level ◽  
Nash Bargaining ◽  
Game Of Chicken ◽  
Nash Bargaining Game ◽  
Satisfactory Account ◽  
Environmental Events ◽  
Natural Classes

AbstractSocial norms regulate and coordinate most aspects of human social life, yet they emerge and change as a result of individual behaviours, beliefs, and expectations. A satisfactory account for the evolutionary dynamics of social norms therefore has to link individual beliefs and expectations to population-level dynamics, where individual norms change according to their consequences for individuals. Here we present a new model of evolutionary dynamics of social norms that encompasses this objective and addresses the emergence of social norms. In this model, a norm is a set of behavioural prescriptions and a set of environmental descriptions that describe the expected behaviours of those with whom the norm holder will interact. These pre-scriptions and descriptions are functions of exogenous environmental events. These events have no intrinsic meaning or effect on the payoffs to individuals, yet beliefs/- superstitions regarding them can effectuate coordination. Though a norm's prescriptions and descriptions are dependent upon one another, we show how they emerge from random accumulations of beliefs. We categorize the space of social norms into several natural classes and study the evolutionary competition between these classes of norms. We apply our model to the Game of Chicken and the Nash Bargaining Game. Further, we show how the space of norms and evolutionary stability is dependent upon the correlation structure of the environment, and under which such correlation structures social dilemmas can be ameliorated or exacerbated.

scholarly journals The Natural Classes of Two-Handed Signs

1998 ◽  
Vol 24 (1) ◽  
pp. 256
Author(s):  
Janine Toole ◽  
Linda Uyechi
Keyword(s):  
Annual Meeting ◽  
General Session ◽  
Natural Classes

Proceedings of the Twenty-Fourth Annual Meeting of the Berkeley Linguistics Society: General Session and Parasession on Phonetics and Phonological Universals (1998)

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