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161.
Yoshihito Tanaka 《Studia Logica》2007,86(1):111-131
It is known that for any subdirectly irreducible finite Heyting algebra A and any Heyting algebra B, A is embeddable into a quotient algebra of B, if and only if Jankov’s formula χ
A
for A is refuted in B. In this paper, we present an infinitary extension of the above theorem given by Jankov. More precisely, for any cardinal
number κ, we present Jankov’s theorem for homomorphisms preserving infinite meets and joins, a class of subdirectly irreducible
complete κ-Heyting algebras and κ-infinitary logic, where a κ-Heyting algebra is a Heyting algebra A with # ≥ κ and κ-infinitary
logic is the infinitary logic such that for any set Θ of formulas with # Θ ≥ κ, ∨Θ and ∧Θ are well defined formulas. 相似文献
162.
Denis Béchet 《Studia Logica》2007,87(2-3):199-224
The paper presents a way to transform pregroup grammars into contextfree grammars using functional composition. The same technique can also be used for the proof-nets of multiplicative cyclic linear logic and for Lambek calculus allowing
empty premises. 相似文献
163.
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165.
This paper is an attempt to put forward a new kind of partial model for representing belief states. I first introduce some philosophical motivations for working with partial models. Then, I present the standard (total) model proposed by Hintikka, and the partial models studied by Humberstone and Holliday. I then show how to reduce Hintikka’s semantics in order to obtain a partial model which, however, differs from Humberstone’s and Holliday’s. The nature of such differences is assessed, and I provide motivations for using the newly proposed semantics rather than the existing ones. Finally, I review some promising philosophical applications of the ideas developed throughout the discussion. 相似文献
166.
Richard W. Paul 《Argumentation》1989,3(2):197-235
The pace of change in the world is accelerating, yet educational institutions have not kept pace. Indeed, schools have historically been the most static of social institutions, uncritically passing down from generation to generation outmoded didactic, lecture-and-drill-based, models of instruction. Predictable results follow. Students, on the whole, do not learn how to work by, or think for, themselves. They do not learn how to gather, analyze, synthesize and assess information. They do not learn how to analyze the diverse logic of the questions and problems they face and hence how to adjust their thinking to those problems. They do not learn how to enter sympathetically into the thinking of others, nor how to deal rationally with conflicting points of view. They do not learn to become critical readers, writers, speakers and listeners. They do not learn how to use their native languages clearly, precisely, or persuasively. They do not, therefore, become literate, in the proper sense of the word. Neither do they gain much in the way of genuine knowledge since, for the most part, they could not explain the basis for what they believe. They would be hard pressed to explain, for example, which of their beliefs were based on rational assent and which on simple conformity to what they have been told. They have little sense as to how they might critically analyze their own experience, or identify national or group bias in their own thinking. They are much more apt to learn on the basis of irrational than rational modes of thought. They lack the traits of mind of a genuinely educated person: intellectual humility, courage, integrity, perseverance, and faith in reason.Happily, there is a movement in education today striving to address these problems in a global way, with strategies and materials for the modification of instruction at all levels of education. At its foundation is an emerging new theory of knowledge, learning, and literacy, one which recognizes the centrality of independent critical thinking to all substantial learning, one which recognizes that higher-order, multilogical thinking is as important to childhood as to adult learning, and as important to foundational learning in monological as in multilogical disciplines. This educational reform movement is not proposing an educational miracle cure, for its leading proponents recognize that many social and historical forces must come together before the ideals of the critical thinking movement will become a full academic reality. Schools do not exist in a social vacuum. To the extent that the broader society is uncritical so, on the whole, will be society's schools. Nevertheless, the social conditions necessary for fundamental changes in schooling are increasingly apparent. The pressure for fundamental change is growing. Whether and to what extent these needed basic changes will be delayed or side-tracked, thus requiring new periodic resurgences of this movement, with new, more elaborate articulations of its ideals, goals, and methods — only time will tell. 相似文献
167.
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169.
Martin Amerbauer 《Studia Logica》1996,57(2-3):359-372
We give sound and complete tableau and sequent calculi for the prepositional normal modal logics S4.04, K4B and G
0(these logics are the smallest normal modal logics containing K and the schemata A A, A A and A ( A); A A and AA; A A and ((A A) A) A resp.) with the following properties: the calculi for S4.04 and G
0are cut-free and have the interpolation property, the calculus for K4B contains a restricted version of the cut-rule, the so-called analytical cut-rule.In addition we show that G
0is not compact (and therefore not canonical), and we proof with the tableau-method that G
0is characterised by the class of all finite, (transitive) trees of degenerate or simple clusters of worlds; therefore G
0is decidable and also characterised by the class of all frames for G
0.Research supported by Fonds zur Förderung der wissenschaftlichen Forschung, project number P8495-PHY.Presented by W. Rautenberg 相似文献
170.
A reduction rule is introduced as a transformation of proof figures in implicational classical logic. Proof figures are represented as typed terms in a -calculus with a new constant P
(()). It is shown that all terms with the same type are equivalent with respect to -reduction augmented by this P-reduction rule. Hence all the proofs of the same implicational formula are equivalent. It is also shown that strong normalization fails for P-reduction. Weak normalization is shown for P-reduction with another reduction rule which simplifies of (( ) ) into an atomic type.This work was partially supported by a Grant-in-Aid for General Scientific Research No. 05680276 of the Ministry of Education, Science and Culture, Japan and by Japan Society for the Promotion of Science.
Hiroakira Ono 相似文献