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1.
Ulrich Meyer 《Journal of Philosophical Logic》2009,38(2):229-247
According to Hans Kamp and Frank Vlach, the two-dimensional tense operators “now” and “then” are ineliminable in quantified
tense logic. This is often adduced as an argument against tense logic, and in favor of an extensional account that makes use
of explicit quantification over times. The aim of this paper is to defend tense logic against this attack. It shows that “now”
and “then” are eliminable in quantified tense logic, provided we endow it with enough quantificational structure. The operators might not
be redundant in some other systems of tense logic, but this merely indicates a lack of quantificational resources and does
not show any deep-seated inability of tense logic to express claims about time. The paper closes with a brief discussion of
the modal analogue of this issue, which concerns the role of the actuality operator in quantified modal logic. 相似文献
2.
This paper presents a new modal logic for ceteris paribus preferences understood in the sense of “all other things being equal”. This reading goes back to the seminal work of Von
Wright in the early 1960’s and has returned in computer science in the 1990’s and in more abstract “dependency logics” today.
We show how it differs from ceteris paribus as “all other things being normal”, which is used in contexts with preference defeaters. We provide a semantic analysis and
several completeness theorems. We show how our system links up with Von Wright’s work, and how it applies to game-theoretic
solution concepts, to agenda setting in investigation, and to preference change. We finally consider its relation with infinitary
modal logics. 相似文献
3.
Deductive inference is usually regarded as being “tautological” or “analytical”: the information conveyed by the conclusion
is contained in the information conveyed by the premises. This idea, however, clashes with the undecidability of first-order
logic and with the (likely) intractability of Boolean logic. In this article, we address the problem both from the semantic
and the proof-theoretical point of view. We propose a hierarchy of propositional logics that are all tractable (i.e. decidable
in polynomial time), although by means of growing computational resources, and converge towards classical propositional logic.
The underlying claim is that this hierarchy can be used to represent increasing levels of “depth” or “informativeness” of
Boolean reasoning. Special attention is paid to the most basic logic in this hierarchy, the pure “intelim logic”, which satisfies
all the requirements of a natural deduction system (allowing both introduction and elimination rules for each logical operator)
while admitting of a feasible (quadratic) decision procedure. We argue that this logic is “analytic” in a particularly strict
sense, in that it rules out any use of “virtual information”, which is chiefly responsible for the combinatorial explosion
of standard classical systems. As a result, analyticity and tractability are reconciled and growing degrees of computational
complexity are associated with the depth at which the use of virtual information is allowed. 相似文献
4.
5.
Alasdair Urquhart 《Journal of Philosophical Logic》2010,39(4):453-472
Quine has argued that modal logic began with the sin of confusing use and mention. Anderson and Belnap, on the other hand,
have offered us a way out through a strategy of nominalization. This paper reviews the history of Lewis’s early work in modal
logic, and then proves some results about the system in which “A is necessary” is intepreted as “A is a classical tautology.” 相似文献
6.
Albert J. J. Anglberger 《Studia Logica》2008,89(3):427-435
In Meyer’s promising account [7] deontic logic is reduced to a dynamic logic. Meyer claims that with his account “we get rid
of most (if not all) of the nasty paradoxes that have plagued traditional deontic logic.” But as was shown by van der Meyden
in [4], Meyer’s logic also contains a paradoxical formula. In this paper we will show that another paradox can be proven,
one which also effects Meyer’s “solution” to contrary to duty obligations and his logic in general.
Presented by Hannes Leitgeb 相似文献
7.
In the paper we explore the idea of describing Pawlak’s rough sets using three-valued logic, whereby the value t corresponds to the positive region of a set, the value f — to the negative region, and the undefined value u — to the border of the set. Due to the properties of the above regions in rough set theory, the semantics of the logic is
described using a non-deterministic matrix (Nmatrix). With the strong semantics, where only the value t is treated as designated, the above logic is a “common denominator” for Kleene and Łukasiewicz 3-valued logics, which represent
its two different “determinizations”. In turn, the weak semantics—where both t and u are treated as designated—represents such a “common denominator” for two major 3-valued paraconsistent logics.
We give sound and complete, cut-free sequent calculi for both versions of the logic generated by the rough set Nmatrix. Then
we derive from these calculi sequent calculi with the same properties for the various “determinizations” of those two versions
of the logic (including Łukasiewicz 3-valued logic). Finally, we show how to embed the four above-mentioned determinizations
in extensions of the basic rough set logics obtained by adding to those logics a special two-valued “definedness” or “crispness”
operator. 相似文献
8.
Zhongtang Cheng 《Frontiers of Philosophy in China》2007,2(2):188-205
This article describes the logic paradigm in the “Mobian” 墨辩 (the debate theory of the Mohist school) investigation from the point of view of hermeneutics, discloses the relationship
between the overinterpretation tradition in China and the logic paradigm in the “Mobian” investigation, observes the overinterpretation of the “Mobian” by the creators and supporters of the logic paradigm from Liang Qichao and Hu Shi to the modernists, including mathematical
logicians, and analyzes Shen Youding’s reflections on the logic paradigm in his later life.
Translated by Huang Deyuan (proofread by Hsiung Ming) from Xueshu Yanjiu 学术研究 (Academic Research Journal), 2005, (1): 49–56 相似文献
9.
We formalise a notion of dynamic rationality in terms of a logic of conditional beliefs on (doxastic) plausibility models.
Similarly to other epistemic statements (e.g. negations of Moore sentences and of Muddy Children announcements), dynamic rationality
changes its meaning after every act of learning, and it may become true after players learn it is false. Applying this to
extensive games, we “simulate” the play of a game as a succession of dynamic updates of the original plausibility model: the
epistemic situation when a given node is reached can be thought of as the result of a joint act of learning (via public announcements)
that the node is reached. We then use the notion of “stable belief”, i.e. belief that is preserved during the play of the
game, in order to give an epistemic condition for backward induction: rationality and common knowledge of stable belief in
rationality. This condition is weaker than Aumann’s and compatible with the implicit assumptions (the “epistemic openness
of the future”) underlying Stalnaker’s criticism of Aumann’s proof. The “dynamic” nature of our concept of rationality explains
why our condition avoids the apparent circularity of the “backward induction paradox”: it is consistent to (continue to) believe
in a player’s rationality after updating with his irrationality. 相似文献
10.
We study an application of gaggle theory to unary negative modal operators. First we treat negation as impossibility and get
a minimal logic system Ki that has a perp semantics. Dunn's kite of different negations can be dealt with in the extensions
of this basic logic Ki. Next we treat negation as “unnecessity” and use a characteristic semantics for different negations in a kite which is dual
to Dunn's original one. Ku is the minimal logic that has a characteristic semantics. We also show that Shramko's falsification logic FL can be incorporated into some extension of this basic logic Ku. Finally, we unite the two basic logics Ki and Ku together to get a negative modal logic K-, which is dual to the positive modal logic K+ in [7]. Shramko has suggested an extension of Dunn's kite and also a dual version in [12]. He also suggested combining them
into a “united” kite. We give a united semantics for this united kite of negations. 相似文献
11.
We investigate the discrete (finite) case of the Popper–Renyi theory of conditional probability, introducing discrete conditional probabilistic models for knowledge and conditional belief, and comparing them with the more standard plausibility models. We also consider a related notion, that of safe belief, which is a weak (non-negatively introspective) type of “knowledge”. We develop a probabilistic version of this concept (“degree
of safety”) and we analyze its role in games. We completely axiomatize the logic of conditional belief, knowledge and safe
belief over conditional probabilistic models. We develop a theory of probabilistic dynamic belief revision, introducing probabilistic
“action models” and proposing a notion of probabilistic update product, that comes together with appropriate reduction laws. 相似文献
12.
Tomoyuki Yamada 《Synthese》2008,165(2):295-315
In this paper, illocutionary acts of commanding will be differentiated from perlocutionary acts that affect preferences of
addressees in a new dynamic logic which combines the preference upgrade introduced in DEUL (dynamic epistemic upgrade logic) by van Benthem and Liu with the deontic update introduced in ECL II (eliminative command logic II) by Yamada. The resulting logic will incorporate J. L. Austin’s distinction between illocutionary
acts as acts having mere conventional effects and perlocutionary acts as acts having real effects upon attitudes and actions
of agents, and help us understand why saying so can make it so in explicit performative utterances. We will also discuss how
acts of commanding give rise to so-called “deontic dilemmas” and how we can accommodate most deontic dilemmas without triggering
so-called “deontic explosion”. 相似文献
13.
Markus Knauff 《Topoi》2007,26(1):19-36
The aim of this article is to strengthen links between cognitive brain research and formal logic. The work covers three fundamental
sorts of logical inferences: reasoning in the propositional calculus, i.e. inferences with the conditional “if...then”, reasoning
in the predicate calculus, i.e. inferences based on quantifiers such as “all”, “some”, “none”, and reasoning with n-place
relations. Studies with brain-damaged patients and neuroimaging experiments indicate that such logical inferences are implemented
in overlapping but different bilateral cortical networks, including parts of the fronto-temporal cortex, the posterior parietal
cortex, and the visual cortices. I argue that these findings show that we do not use a single deterministic strategy for solving
logical reasoning problems. This account resolves many disputes about how humans reason logically and why we sometimes deviate
from the norms of formal logic.
相似文献
Markus KnauffEmail: |
14.
In this paper we show how recent concepts from Dynamic Logic, and in particular from Dynamic Epistemic logic, can be used
to model and interpret quantum behavior. Our main thesis is that all the non-classical properties of quantum systems are explainable
in terms of the non-classical flow of quantum information. We give a logical analysis of quantum measurements (formalized using modal operators) as triggers for quantum information
flow, and we compare them with other logical operators previously used to model various forms of classical information flow:
the “test” operator from Dynamic Logic, the “announcement” operator from Dynamic Epistemic Logic and the “revision” operator
from Belief Revision theory. The main points stressed in our investigation are the following: (1) The perspective and the techniques of “logical dynamics” are useful for understanding quantum information flow. (2) Quantum mechanics does not require any modification of the classical
laws of “static” propositional logic, but only a non-classical dynamics of information. (3) The main such non-classical feature is that, in a quantum world, all information-gathering actions have some ontic side-effects. (4) This ontic impact can affect in its turn the flow of information, leading to non-classical epistemic side-effects (e.g. a type of non-monotonicity) and to states of “objectively imperfect information”. (5) Moreover, the ontic impact is non-local: an information-gathering action on one part of a quantum system can have ontic side-effects on other, far-away parts of
the system. 相似文献
15.
Giangiacomo Gerla 《Studia Logica》2007,86(1):69-87
We define the notion of “potential existence” by starting from the fact that in multi-valued logic the existential quantifier
is interpreted by the least upper bound operator. Besides, we try to define in a general way how to pass from potential into
actual existence.
Presented by Melvin Fitting 相似文献
16.
Dynamic epistemic logic with branching temporal structures 总被引:1,自引:0,他引:1
van Bentham et al. (Merging frameworks for interaction: DEL and ETL, 2007) provides a framework for generating the models
of Epistemic Temporal Logic (ETL: Fagin et al., Reasoning about knowledge, 1995; Parikh and Ramanujam, Journal of Logic, Language, and Information, 2003)
from the models of Dynamic Epistemic Logic (DEL: Baltag et al., in: Gilboa (ed.) Tark 1998, 1998; Gerbrandy, Bisimulations on Planet Kripke, 1999). We consider the logic
TDEL on the merged semantic framework, and its extension with the labeled past-operator “P
ϵ” (“The event ϵ has happened before which. . .”). To axiomatize the extension, we introduce a method for transforming a given
model into a normal form in a suitable sense. These logics suggest further applications of DEL in the theory of agency, the theory of learning, etc. 相似文献
17.
de Freitas Renata P. Viana Jorge P. Benevides Mario R. F. Veloso Sheila R. M. Veloso Paulo A. S. 《Journal of Philosophical Logic》2003,32(4):343-355
In this paper we show that the class of fork squares has a complete orthodox axiomatization in fork arrow logic (FAL). This result may be seen as an orthodox counterpart of Venema's non-orthodox axiomatization for the class of squares in arrow logic. FAL is the modal logic of fork algebras (FAs) just as arrow logic is the modal logic of relation algebras (RAs). FAs extend RAs by a binary fork operator and are axiomatized by adding three equations to RAs equational axiomatization. A proper FA is an algebra of relations where the fork is induced by an injective operation coding pair formation. In contrast to RAs, FAs are representable by proper ones and their equational theory has the expressive power of full first-order logic. A square semantics (the set of arrows is U×U for some set U) for arrow logic was defined by Y. Venema. Due to the negative results about the finite axiomatizability of representable RAs, Venema provided a non-orthodox finite axiomatization for arrow logic by adding a new rule governing the applications of a difference operator. We address here the question of extending the type of relational structures to define orthodox axiomatizations for the class of squares. Given the connections between this problem and the finitization problem addressed by I. Németi, we suspect that this cannot be done by using only logical operations. The modal version of the FA equations provides an orthodox axiomatization for FAL which is complete in view of the representability of FAs. Here we review this result and carry it further to prove that this orthodox axiomatization for FAL also axiomatizes the class of fork squares. 相似文献
18.
Formal nonmonotonic systems try to model the phenomenon that common sense reasoners are able to “jump” in their reasoning
from assumptions Δ to conclusions C without their being any deductive chain from Δ to C. Such jumps are done by various mechanisms which are strongly dependent on context and knowledge of how the actual world
functions. Our aim is to motivate these jump rules as inference rules designed to optimise survival in an environment with
scant resources of effort and time. We begin with a general discussion and quickly move to Section 3 where we introduce five
resource principles. We show that these principles lead to some well known nonmonotonic systems such as Nute’s defeasible
logic. We also give several examples of practical reasoning situations to illustrate our principles.
Edited by Hannes Leitgeb 相似文献
19.
Nuel Belnap 《Studia Logica》2009,91(3):305-334
The first section (§1) of this essay defends reliance on truth values against those who, on nominalistic grounds, would uniformly
substitute a truth predicate. I rehearse some practical, Carnapian advantages of working with truth values in logic. In the
second section (§2), after introducing the key idea of auxiliary parameters (§2.1), I look at several cases in which logics
involve, as part of their semantics, an extra auxiliary parameter to which truth is relativized, a parameter that caters to
special kinds of sentences. In many cases, this facility is said to produce truth values for sentences that on the face of
it seem neither true nor false. Often enough, in this situation appeal is made to the method of supervaluations, which operate
by “quantifying out” auxiliary parameters, and thereby produce something like a truth value. Logics of this kind exhibit striking
differences. I first consider the role that Tarski gives to supervaluation in first order logic (§2.2), and then, after an
interlude that asks whether neither-true-nor-false is itself a truth value (§2.3), I consider sentences with non-denoting
terms (§2.4), vague sentences (§2.5), ambiguous sentences (§2.6), paradoxical sentences (§2.7), and future-tensed sentences
in indeterministic tense logic (§2.8). I conclude my survey with a look at alethic modal logic considered as a cousin (§2.9),
and finish with a few sentences of “advice to supervaluationists” (2.10), advice that is largely negative. The case for supervaluations
as a road to truth is strong only when the auxiliary parameter that is “quantified out” is in fact irrelevant to the sentences of interest—as
in Tarski’s definition of truth for classical logic. In all other cases, the best policy when reporting the results of supervaluation is to use only explicit
phrases such as “settled true” or “determinately true,” never dropping the qualification. 相似文献
20.
Francis J. Pelletier 《Studia Logica》1993,52(2):291-308
THINKER is an automated natural deduction first-order theorem proving program. This paper reports on how it was adapted so as to prove theorems in modal logic. The method employed is an indirect semantic method, obtained by considering the semantic conditions involved in being a valid argument in these modal logics. The method is extended from propositional modal logic to predicate modal logic, and issues concerning the domain of quantification and existence in a world's domain are discussed. Finally, we look at the very interesting issues involved with adding identity to the theorem prover in the realm of modal predicate logic. Various alternatives are discussed. 相似文献