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11.
Norihiro Kamide 《Studia Logica》2009,91(2):217-238
New propositional and first-order paraconsistent logics (called L
ω
and FL
ω
, respectively) are introduced as Gentzen-type sequent calculi with classical and paraconsistent negations. The embedding
theorems of L
ω
and FL
ω
into propositional (first-order, respectively) classical logic are shown, and the completeness theorems with respect to simple
semantics for L
ω
and FL
ω
are proved. The cut-elimination theorems for L
ω
and FL
ω
are shown using both syntactical ways via the embedding theorems and semantical ways via the completeness theorems.
Presented by Yaroslav Shramko and Heinrich Wansing 相似文献
12.
A similarity relation is a reflexive and symmetric binary relation between objects. Similarity is relative: it depends on the set of properties of objects used in determining their similarity or dissimilarity. A multi-modal logical language for reasoning about relative similarities is presented. The modalities correspond semantically to the upper and lower approximations of a set of objects by similarity relations corresponding to all subsets of a given set of properties of objects. A complete deduction system for the language is presented. 相似文献
13.
Given a 1-ary sentence operator , we describe L - another 1-ary operator - as as a left inverse of in a given logic if in that logic every formula is provably equivalent to L. Similarly R is a right inverse of if is always provably equivalent to R. We investigate the behaviour of left and right inverses for taken as the operator of various normal modal logics, paying particular attention to the conditions under which these logics are conservatively extended by the addition of such inverses, as well as to the question of when, in such extensions, the inverses behave as normal modal operators in their own right. 相似文献
14.
On Some Varieties of MTL-algebras 总被引:1,自引:0,他引:1
15.
A. F. Mackay 《The Journal of Ethics》2005,9(3-4):533-549
In the Nicomachean Ethics, Aristotle appears to use an elegant short argument to attack Plato’s doctrine of the good, which argument equally appears to attack Aristotle’s own doctrine of the good. I consider these two questions: First: Why does Aristotle reverse the judgment of Socrates/Plato on the issue: Which is better – things that are (only) good in themselves, or things that are both good in themselves and good for their consequences? Second: Why does Aristotle attack Plato’s doctrine that the Form of the Good is the chief good, with an argument that appears to threaten his own view that eudaimonia is the chief good? I think the answers to these two questions are related. The elegant short argument in question I call “Aristotle’s Fast Argument.”After apologizing for criticizing views held by friends of his, Aristotle deploys the Fast Argument as a clincher to cap off his refutation of Plato’s view that the Form of the Good is the chief good: “And one might ask the question, what in the world they mean by ‘a thing itself’, if in man himself and in a particular man the account of man is one and the same. For in so far as they are men, they will in no respect differ; and if this is so, neither will there be a difference in so far as they are good. But again it will not be good any the more for being eternal, since that which lasts long is no whiter than that which perishes in a day.” (Aristotle, Nichomachean Ethics, 1096 a34–b4). I explore this sketchily presented Fast Argument. I consider why Aristotle may think it is valid and why he does not seem to realize that, on readings that make it effective against Plato’s view, his Fast Argument also seems to apply to his own view that eudaimonia is the chief good. This is what I will call “Aristotle’s Dilemma.” If the Fast Argument is interpreted too narrowly, its point about the whiteness of a white thing being independent of its duration will not apply to the goodness of the Form of the Good. If it is interpreted broadly enough to undermine the claim of the Form of the Good to be the chief good, it will equally undermine that claim for eudaimonia. Finally, I discuss some of the things Plato and Aristotle say about the chief good, and comparable things Immanuel Kant says about the good will. I draw some speculative conclusions that focus on the importance for Aristotle of the goodness of the chief good not being at risk. 相似文献
16.
Logics with the Qualitative Probability Operator 总被引:2,自引:0,他引:2
Ognjanovic Zoran; Perovic Aleksandar; Raskovic Miodrag 《Logic Journal of the IGPL》2008,16(2):105-120
The paper presents several strongly complete axiomatizationsof qualitative probability within the framework of probabilisticlogic. We show that in the proposed semantics qualitative probabilitiesare characterized by probability functions, so they also arecomparative probabilities. 相似文献
17.
D. C. McCarty 《Journal of Philosophical Logic》1996,25(5):559-565
Let S be a deductive system such that S-derivability (s) is arithmetic and sound with respect to structures of class K. From simple conditions on K and s, it follows constructively that the K-completeness of s implies MP(S), a form of Markov's Principle. If s is undecidable then MP(S) is independent of first-order Heyting arithmetic. Also, if s is undecidable and the S proof relation is decidable, then MP(S) is independent of second-order Heyting arithmetic, HAS. Lastly, when s is many-one complete, MP(S) implies the usual Markov's Principle MP.An immediate corollary is that the Tarski, Beth and Kripke weak completeness theorems for the negative fragment of intuitionistic predicate logic are unobtainable in HAS. Second, each of these: weak completeness for classical predicate logic, weak completeness for the negative fragment of intuitionistic predicate logic and strong completeness for sentential logic implics MP. Beth and Kripke completeness for intuitionistic predicate or sentential logic also entail MP.These results give extensions of the theorem of Gödel and Kreisel (in [4]) that completeness for pure intuitionistic predicate logic requires MP. The assumptions of Gödel and Kreisel's original proof included the Axiom of Dependent Choice and Herbrand's Theorem, no use of which is explicit in the present article. 相似文献
18.
In this paper, a theorem on the existence of complete embedding of partially ordered monoids into complete residuated lattices is shown. From this, many interesting results on residuated lattices and substructural logics follow, including various types of completeness theorems of substructural logics. 相似文献
19.
Standard Kripke models are inadequate to model situations of inexact knowledge with introspection, since positive and negative
introspection force the relation of epistemic indiscernibility to be transitive and euclidean. Correlatively, Williamson’s
margin for error semantics for inexact knowledge invalidates axioms 4 and 5. We present a new semantics for modal logic which
is shown to be complete for K45, without constraining the accessibility relation to be transitive or euclidean. The semantics corresponds to a system of
modular knowledge, in which iterated modalities and simple modalities are not on a par. We show how the semantics helps to
solve Williamson’s luminosity paradox, and argue that it corresponds to an integrated model of perceptual and introspective
knowledge that is psychologically more plausible than the one defended by Williamson. We formulate a generalized version of
the semantics, called token semantics, in which modalities are iteration-sensitive up to degree n and insensitive beyond n. The multi-agent version of the semantics yields a resource-sensitive logic with implications for the representation of common
knowledge in situations of bounded rationality. 相似文献
20.
Subjective Situations and Logical Omniscience 总被引:1,自引:0,他引:1
The beliefs of the agents in a multi-agent system have been formally modelled in the last decades using doxastic logics. The possible worlds model and its associated Kripke semantics provide an intuitive semantics for these logics, but they commit us to model agents that are logically omniscient. We propose a way of avoiding this problem, using a new kind of entities called subjective situations. We define a new doxastic logic based on these entities and we show how the belief operators have some desirable properties, while avoiding logical omniscience. A comparison with two well-known proposals (Levesque's logic of explicit and implicit beliefs and Thijsse's hybrid sieve systems) is also provided. 相似文献