共查询到10条相似文献,搜索用时 171 毫秒
1.
J. Sakalauskaitė 《Lithuanian Mathematical Journal》2007,47(3):266-276
In this paper, we consider branching time temporal logic CT L with epistemic modalities for knowledge (belief) and with awareness operators. These logics involve the discrete-time linear
temporal logic operators “next” and “until” with the branching temporal logic operator “on all paths”. In addition, the temporal
logic of knowledge (belief) contains an indexed set of unary modal operators “agent i knows” (“agent i believes”). In a language of these logics, there are awareness operators. For these logics, we present sequent calculi with
a restricted cut rule. Thus, we get proof systems where proof-search becomes decidable. The soundness and completeness for
these calculi are proved.
Published in Lietuvos Matematikos Rinkinys, Vol. 47, No. 3, pp. 328–340, July–September, 2007. 相似文献
2.
Daniele Castorina Pierpaolo Esposito Berardino Sciunzi 《Calculus of Variations and Partial Differential Equations》2009,34(3):279-306
The behavior of the “minimal branch” is investigated for quasilinear eigenvalue problems involving the p-Laplace operator, considered in a smooth bounded domain of , and compactness holds below a critical dimension N
#. The nonlinearity f(u) lies in a very general class and the results we present are new even for p = 2. Due to the degeneracy of p-Laplace operator, for p ≠ 2 it is crucial to define a suitable notion of semi-stability: the functional space we introduce in the paper seems to
be the natural one and yields to a spectral theory for the linearized operator. For the case p = 2, compactness is also established along unstable branches satisfying suitable spectral information. The analysis is based
on a blow-up argument and stronger assumptions on the nonlinearity f(u) are required.
Authors are partially supported by MIUR, project “Variational methods and nonlinear differential equations”. 相似文献
3.
Alessio Moretti 《Logica Universalis》2009,3(1):19-57
Whereas geometrical oppositions (logical squares and hexagons) have been so far investigated in many fields of modal logic
(both abstract and applied), the oppositional geometrical side of “deontic logic” (the logic of “obligatory”, “forbidden”,
“permitted”, . . .) has rather been neglected. Besides the classical “deontic square” (the deontic counterpart of Aristotle’s
“logical square”), some interesting attempts have nevertheless been made to deepen the geometrical investigation of the deontic
oppositions: Kalinowski (La logique des normes, PUF, Paris, 1972) has proposed a “deontic hexagon” as being the geometrical
representation of standard deontic logic, whereas Joerden (jointly with Hruschka, in Archiv für Rechtsund Sozialphilosophie
73:1, 1987), McNamara (Mind 105:419, 1996) and Wessels (Die gute Samariterin. Zur Struktur der Supererogation, Walter de Gruyter,
Berlin, 2002) have proposed some new “deontic polygons” for dealing with conservative extensions of standard deontic logic
internalising the concept of “supererogation”. Since 2004 a new formal science of the geometrical oppositions inside logic
has appeared, that is “n-opposition theory”, or “NOT”, which relies on the notion of “logical bi-simplex of dimension m” (m = n − 1). This theory has received a complete mathematical foundation in 2008, and since then several extensions. In this paper,
by using it, we show that in standard deontic logic there are in fact many more oppositional deontic figures than Kalinowski’s
unique “hexagon of norms” (more ones, and more complex ones, geometrically speaking: “deontic squares”, “deontic hexagons”,
“deontic cubes”, . . ., “deontic tetraicosahedra”, . . .): the real geometry of the oppositions between deontic modalities
is composed by the aforementioned structures (squares, hexagons, cubes, . . ., tetraicosahedra and hyper-tetraicosahedra),
whose complete mathematical closure happens in fact to be a “deontic 5-dimensional hyper-tetraicosahedron” (an oppositional
very regular solid).
相似文献
4.
We consider the following “silent duel” of m players with a possible economic interpretation. Each player has one “bullet”, which she can shoot at any time during the time interval [0,1]. The probability that the i-th player hits the “target” at moment t is given by an increasing accuracy function f
i
(t). The winner is the player who hits the target first. Under natural assumptions on the functions f
i
(t) we prove the existence and uniqueness of a Nash equilibrium point in this game, and we provide an explicit construction of this equilibrium. This construction allows us to obtain exact solutions for many specific examples. Some of them are presented.This work was partly supported by RBRF grants 03-01-00479. 相似文献
5.
Tommaso Flaminio 《Archive for Mathematical Logic》2007,46(3-4):301-319
In this paper we investigate the problem of testing the coherence of an assessment of conditional probability following a
purely logical setting. In particular we will prove that the coherence of an assessment of conditional probability χ can be
characterized by means of the logical consistency of a suitable theory T
χ defined on the modal-fuzzy logic FP
k
(RŁΔ) built up over the many-valued logic RŁΔ. Such modal-fuzzy logic was previously introduced in Flaminio (Lecture Notes in Computer Science, vol. 3571, 2005) in order
to treat conditional probability by means of a list of simple probabilities following the well known (smart) ideas exposed
by Halpern (Proceedings of the eighth conference on theoretical aspects of rationality and knowledge, pp 17–30, 2001) and
by Coletti and Scozzafava (Trends Logic 15, 2002). Roughly speaking, such logic is obtained by adding to the language of RŁΔ a list of k modalities for “probably” and axioms reflecting the properties of simple probability measures. Moreover we prove that the satisfiability problem for
modal formulas of FP
k
(RŁΔ) is NP-complete. Finally, as main result of this paper, we prove FP
k
(RŁΔ) in order to prove that the problem of establishing the coherence of rational assessments of conditional probability is NP-complete.
相似文献
6.
Stephen Morris 《International Journal of Game Theory》1999,28(3):385-408
Suppose we replace “knowledge” by “belief with probability p” in standard definitions of common knowledge. Very different notions arise depending on the exact definition of common knowledge
used in the substitution. This paper demonstrates those differences and identifies which notion is relevant in each of three
contexts: equilibrium analysis in incomplete information games, best response dynamics in incomplete information games, and
agreeing to disagree/no trade results. 相似文献
7.
Ivan Chajda 《Central European Journal of Mathematics》2011,9(5):1185-1191
We introduce two unary operators G and H on a relatively pseudocomplemented lattice which form an algebraic axiomatization of the tense quantifiers “it is always
going to be the case that” and “it has always been the case that”. Their axiomatization is an extended version for the classical
logic and it is in accordance with these operators on many-valued Łukasiewicz logic. Finally, we get a general construction
of these tense operators on complete relatively pseudocomplemented lattice which is a power lattice via the so-called frame. 相似文献
8.
Johann C. Marek 《Acta Analytica》2011,26(1):53-61
Experiences are interpreted as conscious mental occurrences that are of phenomenal character. There is already a kind of (weak)
intentionality involved with this phenomenal interpretation. A stricter conception of experiences distinguishes between purely
phenomenal experiences and intentional experiences in a narrow sense. Wittgenstein’s account of psychological (experiential)
verbs is taken over: Usually, expressing mental states verbally is not describing them. According to this, “I believe” can
be seen as an expression of one’s own belief, but not as an expression of a belief about one’s belief. Hence, the utterance
“I believe it is raining” shows that I believe that it is raining, although it is not said by these words that I believe that it is raining. Thinking thoughts such as “I believe it is raining, but it is not raining”
(a variant of Moore’s paradox) is an absurdity between what is already said by silently uttering “It is not raining” and what
is shown by silently uttering “I believe it is raining.” The paper agrees with a main result of Wittgenstein’s considerations
of Moore’s paradox, namely the view that logical structure, deducibility, and consistency cannot be reduced solely to propositions—besides
a logic of propositions, there is, for example, a logic of assertions and of imperatives, respectively. 相似文献
9.
John-Michael Kuczynski 《Acta Analytica》2004,19(32):107-141
Recently, many have argued that phenomenal content supervenes on representational content; i.e. that the phenomenal character of an experience is wholly determined (metaphysically, not
causally) by the representational content of that experience. This paper it identifies many counter-examples to intentionalism.
Further, this paper shows that, if intentionalism were correct, that would require that an untenable form of representational
atomism also be correct. Our argument works both against the idea that phenomenal content supervenes on “conceptual” content
and also against the idea that it supervenes on “non-conceptual” content. It is also shown that the distinction between conceptual
and non-conceptual content has been wrongly conceived as distinction between different kinds of information: in fact, it is
a distinction between ways of packaging information that is, in itself, neither conceptual or non-conceptual. 相似文献
10.
We demonstrate that, if there are sufficiently many players, any Bayesian equilibrium of an incomplete information game can
be “ε-purified” . That is, close to any Bayesian equilibrium there is an approximate Bayesian equilibrium in pure strategies. Our
main contribution is obtaining this result for games with a countable set of pure strategies. In order to do so we derive
a mathematical result, in the spirit of the Shapley–Folkman Theorem, permitting countable strategy sets. Our main assumption
is a “large game property,” dictating that the actions of relatively small subsets of players cannot have large affects on
the payoffs of other players.
E. Cartwright and M. Wooders are indebted to Phillip Reny, Frank Page and two anonymous referees for helpful comments. 相似文献