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1.
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
2.
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
3.
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
4.
Xuefeng Wen 《Studia Logica》2007,85(2):251-260
We construct a a system PLRI which is the classical propositional logic supplied with a ternary construction , interpreted as the intensional identity of statements and in the context . PLRI is a refinement of Roman Suszko’s sentential calculus with identity (SCI) whose identity connective is a binary one.
We provide a Hilbert-style axiomatization of this logic and prove its soundness and completeness with respect to some algebraic
models. We also show that PLRI can be used to give a partial solution to the paradox of analysis.
Presented by Jacek Malinowski 相似文献
5.
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
6.
This paper presents a calculus for mereotopological reasoning in which two-dimensional spatial regions are treated as primitive entities. A first order predicate language
with a distinguished unary predicate c(x), function-symbols , · and – and constants 0 and 1 is defined. An interpretation
for
is provided in which polygonal open subsets of the real plane serve as elements of the domain. Under this interpretation the predicate c(x) is read as region x is connected and the function-symbols and constants are given their meaning in terms of a Boolean algebra of polygons. We give an alternative interpretation
based on the real closed plane which turns out to be isomorphic to
A set of axioms and a rule of inference are introduced. We prove the soundness and completeness of the calculus with respect to the given interpretation. 相似文献
7.
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
8.
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
9.
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
10.
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
11.
S. K. Thomason 《Journal of Philosophical Logic》1989,18(1):43-67
Conclusions and conjectures Some may be of the opinion that one event can begin before another only by virtue of the existence of some event (a witness) which wholly precedes the other and does not wholly precede the one (and similarly for ends before and does not abut). Those would prefer
0 to
as a model for observers' apprehensions of events. Since G is a functor from
to
0, the current construction (restricted to
0) remains applicable.This work supports a claim that the psychologically fundamental temporal relationships are wholly precedes, begins before, ends before and abuts. But only in a very weak sense. Any other set of relationships which is interdefinable with this one, using only quantifier-free formulas in the definitions, could be used to define a category
which is indistinguishable from
(because the same functions preserve and reflect the new relationships). This work equally supports the claim that those relationships are the psychologically fundamental ones, or the claim that it is just wholly precedes which is fundamental, and that we perceive begins before just by virtue of witnesses. But it refutes the claim that only wholly precedes is fundamental, and that we understand begins before only because we understand time as a linear ordering. 相似文献
12.
A logic of intention and attempt 总被引:3,自引:1,他引:2
We present a modal logic called (logic of intention and attempt) in which we can reason about intention dynamics and intentional action execution. By exploiting
the expressive power of , we provide a formal analysis of the relation between intention and action and highlight the pivotal role of attempt in action execution. Besides, we deal with the problems of instrumental reasoning and intention persistence. 相似文献
13.
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
14.
Christopher Steinsvold 《Journal of Philosophical Logic》2008,37(1):45-56
Patrick Grim has presented arguments supporting the intuition that any notion of a totality of truths is incoherent. We suggest
a natural semantics for various logics of belief which reflect Grim’s intuition. The semantics is a topological semantics,
and we suggest that the condition can be interpreted to reflect Grim’s intuition. Beyond this, we present a natural canonical topological model for
K4 and KD4. 相似文献
15.
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
16.
17.
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
18.
In ‘belief revision’ a theory
is revised with a formula φ resulting in a revised theory
. Typically,
is in
, one has to give up belief in
by a process of retraction, and φ is in
. We propose to model belief revision in a dynamic epistemic logic. In this setting, we typically have an information state
(pointed Kripke model) for the theory
wherein the agent believes the negation of the revision formula, i.e., wherein
is true. The revision with φ is a program *φ that transforms this information state into a new information state. The transformation
is described by a dynamic modal operator [*φ], that is interpreted as a binary relation [ [*φ] ] between information states.
The next information state is computed from the current information state and the belief revision formula. If the revision
is successful, the agent believes φ in the resulting state, i.e., Bφ is then true. To make this work, as information states we propose ‘doxastic epistemic models’ that represent both knowledge
and degrees of belief. These are multi-modal and multi-agent Kripke models. They are constructed from preference relations
for agents, and they satisfy various characterizable multi-agent frame properties. Iterated, revocable, and higher-order belief
revision are all quite natural in this setting. We present, for an example, five different ways of such dynamic belief revision.
One can also see that as a non-deterministic epistemic action with two alternatives, where one is preferred over the other,
and there is a natural generalization to general epistemic actions with preferences. 相似文献
19.
Alan L. Gross 《Psychometrika》1981,46(2):161-169
In predicting
scores fromp > 1 observed scores
in a sample of sizeñ, the optimal strategy (minimum expected loss), under certain assumptions, is shown to be based upon the least squares regression weights
computed from a previous sample. Letting
represent the correlation between
and the predicted values
, and letting
represent the correlation between
and a different set of predicted values
, where w is any weighting system which is not a function of
, it is shown that the probability of
being less than
cannot exceed .50. The relationship of this result to previous research and practical implications are discussed. 相似文献
20.
Ming Hsiung 《Journal of Philosophical Logic》2008,37(4):299-317
By introducing the intensional mappings and their properties, we establish a new semantical approach of characterizing intermediate
logics. First prove that this new approach provides a general method of characterizing and comparing logics without changing
the semantical interpretation of implication connective. Then show that it is adequate to characterize all Kripke_complete
intermediate logics by showing that each of these logics is sound and complete with respect to its (unique) ‘weakest characterization
property’ of intensional mappings. In particular, we show that classical logic has the weakest characterization property , which is the strongest among all possible weakest characterization properties of intermediate logics. Finally, it follows
from this result that a translation is an embedding of classical logic into intuitionistic logic, iff. its semantical counterpart
has the property .
相似文献