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1.
We investigate an expansion of quasi-MV algebras ([10]) by a genuine quantum unary operator. The variety of such
quasi-MV algebras has a subquasivariety whose members—called cartesian—can be obtained in an appropriate way out of MV algebras. After showing that cartesian . quasi-MV algebras generate ,we prove a standard completeness theorem for w.r.t. an algebra over the complex numbers.
Presented by Heinrich Wansing 相似文献
2.
We present some equivalent conditions for a quasivariety of structures to be generated by a single structure. The first such condition, called the embedding property was found by A.I. Mal′tsev in [6]. It says that if are nontrivial, then there exists such that A and B are embeddable into C. One of our equivalent conditions states that the set of quasi-identities valid in is closed under a certain Gentzen type rule which is due to J. Łoś and R. Suszko [5].
Presented by Jacek Malinowski 相似文献
3.
Marta A. Zander 《Studia Logica》2008,88(2):233-246
In this paper we prove that, for n > 1, the n-generated free algebra in any locally finite subvariety of HoRA can be written in a unique nontrivial way as Ł2 × A′, where A′ is a directly indecomposable algebra in . More precisely, we prove that the unique nontrivial pair of factor congruences of is given by the filters and , where the element is recursively defined from the term introduced by W. H. Cornish. As an additional result we obtain a characterization of minimal irreducible filters of in terms of its coatoms.
Presented by Daniele Mundici 相似文献
4.
First we show that the classical two-player semantic game actually corresponds to a three-valued logic. Then we generalize
this result and give an n-player semantic game for an n + 1-valued logic with n binary connectives, each associated with a player. We prove that player i has a winning strategy in game if and only if the truth value of is t
i
in the model M, for 1 ≤ i ≤ n; and none of the players has a winning strategy in if and only if the truth value of is t
0 in M. 相似文献
5.
Sato Kentaro 《Studia Logica》2008,88(2):295-324
We study filters in residuated structures that are associated with congruence relations (which we call -filters), and develop a semantical theory for general substructural logics based on the notion of primeness for those filters.
We first generalize Stone’s sheaf representation theorem to general substructural logics and then define the primeness of
-filters as being “points” (or stalkers) of the space, the spectrum, on which the representing sheaf is defined. Prime FL-filters
will turn out to coincide with truth sets under various well known semantics for certain substructural logics. We also investigate
which structural rules are needed to interpret each connective in terms of prime -filters in the same way as in Kripke or Routley-Meyer semantics. We may consider that the set of the structural rules that
each connective needs in this sense reflects the difficulty of giving the meaning of the connective. A surprising discovery
is that connectives , ⅋ of linear logic are linearly ordered in terms of the difficulty in this sense.
Presented by Wojciech Buszkowski 相似文献
6.
J. Michael Dunn 《Studia Logica》1979,38(2):149-169
Given classical (2 valued) structures
and
and a homomorphism h of
onto
, it is shown how to construct a (non-degenerate) 3-valued counterpart
of
. Classical sentences that are true in
are non-false in
. Applications to number theory and type theory (with axiom of infinity) produce finite 3-valued models in which all classically true sentences of these theories are non-false. Connections to relevant logic give absolute consistency proofs for versions of these theories formulated in relevant logic (the proof for number theory was obtained earlier by R. K. Meyer and suggested the present abstract development). 相似文献
7.
Radomír Halaš 《Studia Logica》2008,89(1):19-35
It has been recently shown [4] that the lattice effect algebras can be treated as a subvariety of the variety of so-called
basic algebras. The open problem whether all subdirectly irreducible distributive lattice effect algebras are just subdirectly
irreducible MV-chains and the horizontal sum of two 3-element chains is in the paper transferred into a more tractable one. We prove that modulo distributive lattice
effect algebras, the variety generated by MV-algebras and is definable by three simple identities and the problem now is to check if these identities are satisfied by all distributive
lattice effect algebras or not.
Presented by Daniele Mundici 相似文献
8.
9.
Miklós Ferenczi 《Studia Logica》2007,87(1):1-11
It is known that every α-dimensional quasi polyadic equality algebra (QPEA
α
) can be considered as an α-dimensional cylindric algebra satisfying the merrygo- round properties . The converse of this proposition fails to be true. It is investigated in the paper how to get algebras in QPEA from algebras
in CA. Instead of QPEA the class of the finitary polyadic equality algebras (FPEA) is investigated, this class is definitionally
equivalent to QPEA. It is shown, among others, that from every algebra in a β-dimensional algebra can be obtained in QPEA
β
where , moreover the algebra obtained is representable in a sense.
Presented by Daniele Mundici
Supported by the OTKA grants T0351192, T43242. 相似文献
10.
Two groups of agents, and , face a moral conflict if has a moral obligation and has a moral obligation, such that these obligations cannot both be fulfilled. We study moral conflicts using a multi-agent
deontic logic devised to represent reasoning about sentences like ‘In the interest of group of agents, group of agents ought to see to it that .’ We provide a formal language and a consequentialist semantics. An illustration of our semantics with an analysis of the
Prisoner’s Dilemma follows. Next, necessary and sufficient conditions are given for (1) the possibility that a single group
of agents faces a moral conflict, for (2) the possibility that two groups of agents face a moral conflict within a single
moral code, and for (3) the possibility that two groups of agents face a moral conflict. 相似文献
11.
Heinrich Wansing 《Journal of Philosophical Logic》2006,35(6):653-660
Many logical systems are such that the addition of Prior's binary connective to them leads to triviality, see [1, 8]. Since is given by some introduction and elimination rules in natural deduction or sequent rules in Gentzen's sequent calculus, the unwanted effects of adding show that some kind of restriction has to be imposed on the acceptable operational inferences rules, in particular if these rules are regarded as definitions of the operations concerned. In this paper, a number of simple observations is made showing that the unwanted phenomenon exemplified by in some logics also occurs in contexts in which
is acceptable. In fact, in any non-trivial context, the acceptance of arbitrary introduction rules for logical operations permits operations leading to triviality. Connectives that in all non-trivial contexts lead to triviality will be called non-trivially trivializing connectives. 相似文献
12.
Tarek Sayed Ahmed 《Studia Logica》2007,85(2):139-151
SC, CA, QA and QEA denote the class of Pinter’s substitution algebras, Tarski’s cylindric algebras, Halmos’ quasi-polyadic
and quasi-polyadic equality algebras, respectively. Let . and . We show that the class of n dimensional neat reducts of algebras in K
m
is not elementary. This solves a problem in [2]. Also our result generalizes results proved in [1] and [2].
Presented by Robert Goldblatt 相似文献
13.
An algebra A is said to be congruence coherent if every subalgebra of A that contains a class of some congruence on A is a union of -classes. This property has been investigated in several varieties of lattice-based algebras. These include, for example,
de Morgan algebras, p-algebras, double p-algebras, and double MS-algebras. Here we determine precisely when the property holds in the class of symmetric extended
de Morgan algebras.
Presented by M.E. Adams 相似文献
14.
Marc Pauly 《Synthese》2007,158(2):233-250
We investigate under what conditions a given set of collective judgments can arise from a specific voting procedure. In order
to answer this question, we introduce a language similar to modal logic for reasoning about judgment aggregation procedures.
In this language, the formula
expresses that is collectively accepted, or that is a group judgment based on voting. Different judgment aggregation procedures may be underlying the group decision making.
Here we investigate majority voting, where holds if a majority of individuals accepts, consensus voting, where holds if all individuals accept, and dictatorship. We provide complete axiomatizations for judgment sets arising from all three aggregation procedures. 相似文献
15.
Alexander Budkin 《Studia Logica》2004,78(1-2):107-127
The dominion of a subalgebra H in an universal algebra A (in a class
) is the set of all elements
such that for all homomorphisms
if f, g coincide on H, then af = ag. We investigate the connection between dominions and quasivarieties. We show that if a class
is closed under ultraproducts, then the dominion in
is equal to the dominion in a quasivariety generated by
. Also we find conditions when dominions in a universal algebra form a lattice and study this lattice.Special issue of Studia Logica: Algebraic Theory of Quasivarieties Presented by
M. E. Adams, K. V. Adaricheva, W. Dziobiak, and A. V. Kravchenko 相似文献
16.
Jarosław Achinger 《Studia Logica》1986,45(3):293-300
Universality of generalized Alexandroff's cube
plays essential role in theory of absolute retracts for the category of , -closure spaces. Alexandroff's cube.
is an , -closure space generated by the family of all complete filters. in a lattice of all subsets of a set of power
.Condition P(, ,
) says that
is a closure space of all , -filters in the lattice (
),
.Assuming that P (, ,
) holds, in the paper [2], there are given sufficient conditions saying when an , -closure space is an absolute retract for the category of , -closure spaces (see Theorems 2.1 and 3.4 in [2]).It seems that, under assumption that P (, ,
) holds, it will be possible to givean uniform characterization of absolute retracts for the category of , -closure-spaces.Except Lemma 3.1 from [1], there is no information when the condition P (, ,
) holds or when it does not hold.The main result of this paper says, that there are examples of cardinal numbers, , ,
such that P (, ,
) is not satisfied.Namely it is proved, using elementary properties of Lebesgue measure on the real line, that the condition P (,
1, 2
) is not satisfied.Moreover it is shown that fulfillment of the condition is essential assumption in, Theorems 2.1 and 3.4 from [1] i.e. it cannot be eliminated. 相似文献
17.
The lattices of varieties were studied in many works (see [4], [5], [11], [24], [31]). In this paper we describe the lattice
of all subvarieties of the variety defined by so called externally compatible identities of Abelian groups and the identity x
n
≈ y
n
.
The notation in this paper is the same as in [2].
Presented by W. Dziobiak 相似文献
18.
R. Gregory Taylor 《Journal of Philosophical Logic》2008,37(6):575-591
Symmetric propositions over domain and signature are characterized following Zermelo, and a correlation of such propositions with logical type- quantifiers over is described. Boolean algebras of symmetric propositions over and Σ are shown to be isomorphic to algebras of logical type- quantifiers over . This last result may provide empirical support for Tarski’s claim that logical terms over fixed domain are all and only
those invariant under domain permutations. 相似文献
19.
Let
be a finite collection of finite algebras of finite signature such that SP(
) has meet semi-distributive congruence lattices. We prove that there exists a finite collection
1 of finite algebras of the same signature,
, such that SP(
1) is finitely axiomatizable.We show also that if
, then SP(
1) is finitely axiomatizable. We offer new proofs of two important finite basis theorems of D. Pigozzi and R. Willard. Our actual results are somewhat more general than this abstract indicates.While working on this paper, the first author was partially supported by the Hungarian National Foundation for Scientific Research (OTKA) grant no. T37877 and the second author was supported by the US National Science Foundation grant no. DMS-0245622.Special issue of Studia Logica: Algebraic Theory of Quasivarieties Presented by
M. E. Adams, K. V. Adaricheva, W. Dziobiak, and A. V. Kravchenko 相似文献
20.
Gerard R. Renardel de Lavalette 《Synthese》2008,164(3):437-450
The Interpolation Theorem, first formulated and proved by W. Craig fifty years ago for predicate logic, has been extended
to many other logical frameworks and is being applied in several areas of computer science. We give a short overview, and
focus on the theory of software systems and modules. An algebra of theories TA is presented, with a nonstandard interpretation of the existential quantifier . In TA, the interpolation property of the underlying logic corresponds with the quantifier combination property . It is shown how the Modularization Theorem, the Factorization Lemma and the Normal Form Theorem for module expressions
can be proved in TA.
Dedicated to the 50th anniversary of William Craig’s Interpolation Theorem. 相似文献