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251.
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
252.
Max A. Freund 《Journal of Philosophical Logic》2007,36(5):571-598
We consider a formal language whose logical syntax involves both modal and tense propositional operators, as well as sortal
quantifiers, sortal identities and (second order) quantifiers over sortals. We construct an intensional semantics for the
language and characterize a formal logical system which we prove to be sound and complete with respect to the semantics. Conceptualism
is the philosophical background of the semantic system. 相似文献
253.
Lawrence S. Moss 《Journal of Philosophical Logic》2007,36(6):605-640
This paper obtains the weak completeness and decidability results for standard systems of modal logic using models built from
formulas themselves. This line of work began with Fine (Notre Dame J. Form. Log. 16:229–237, 1975). There are two ways in
which our work advances on that paper: First, the definition of our models is mainly based on the relation Kozen and Parikh
used in their proof of the completeness of PDL, see (Theor. Comp. Sci. 113–118, 1981). The point is to develop a general model-construction
method based on this definition. We do this and thereby obtain the completeness of most of the standard modal systems, and
in addition apply the method to some other systems of interest. None of the results use filtration, but in our final section
we explore the connection. 相似文献
254.
Giangiacomo Gerla 《Journal of Philosophical Logic》2007,36(6):707-733
A metric approach to Popper’s verisimilitude question is proposed which is related to point-free geometry. Indeed, we define
the theory of approximate metric spaces whose primitive notions are regions, inclusion relation, minimum distance, and maximum distance between regions. Then, we show that the class of possible scientific theories has the structure of an approximate metric
space. So, we can define the verisimilitude of a theory as a function of its (approximate) distance from the truth. This avoids
some of the difficulties arising from the known definitions of verisimilitude. 相似文献
255.
256.
257.
《Journal of Applied Logic》2014,12(1):50-66
Relational semantics, given by Kripke frames, play an essential role in the study of modal and intuitionistic logic. In [4] it is shown that the theory of relational semantics is also available in the more general setting of substructural logic, at least in an algebraic guise. Building on these ideas, in [5] a type of frames is described which generalise Kripke frames and provide semantics for substructural logics in a purely relational form.In this paper we study full linear logic from an algebraic point of view. The main additional hurdle is the exponential. We analyse this operation algebraically and use canonical extensions to obtain relational semantics. Thus, we extend the work in [4], [5] and use their approach to obtain relational semantics for full linear logic. Hereby we illustrate the strength of using canonical extension to retrieve relational semantics: it allows a modular and uniform treatment of additional operations and axioms.Traditionally, so-called phase semantics are used as models for (provability in) linear logic [8]. These have the drawback that, contrary to our approach, they do not allow a modular treatment of additional axioms. However, the two approaches are related, as we will explain. 相似文献
258.
《Journal of Applied Logic》2014,12(2):128-150
A logic for specifying probabilistic transition systems is presented. Our perspective is that of agents performing actions. A procedure for deciding whether sentences in this logic are valid is provided. One of the main contributions of the paper is the formulation of the decision procedure: a tableau system which appeals to solving systems of linear equations. The tableau rules eliminate propositional connectives, then, for all open branches of the tableau tree, systems of linear equations are generated and checked for feasibility. Proofs of soundness, completeness and termination of the decision procedure are provided. 相似文献
259.
260.
《Journal of Applied Logic》2015,13(3):285-315
Abduction (ἀπαγωγή, in ancient Greek, often translated as “leading away” or “reduction”) is a procedure in which something that lacks classical explanatory epistemic virtue can be accepted because it has virtue of another kind: Gabbay and Woods [15] contend (GW-schema) that abduction presents an ignorance-preserving or (ignorance-mitigating) character. From this perspective abductive reasoning is a response to an ignorance-problem; through abduction the basic ignorance – that does not have to be considered a total “ignorance” – is neither solved nor left intact. Abductive reasoning is an ignorance-preserving accommodation of the problem at hand. Is abduction really ignorance-preserving? To better answer this question I will introduce (and take advantage of) an eco-cognitive model (EC-Model) of abduction. It will be illustrated that through abduction, knowledge can be enhanced, even when abduction is not considered an inference to the best explanation in the classical sense of the expression, that is an inference necessarily characterized by an empirical evaluation phase, or an inductive phase, as Peirce called it. To further deepen the eco-cognitive character of abduction a simple genealogy of logic is provided: Aristotle clearly states that in syllogistic theory local/environmental cognitive factors – external to that peculiar inferential process, for example regarding users/reasoners, are given up. Indeed, to define syllogism Aristotle first of all insists that all syllogisms are valid and contends that the necessity of this kind of reasoning is related to the circumstance that “no further term from outside (ἔξωθɛν) is needed”, in sum syllogism is the fruit of a kind of eco-cognitive immunization. At the same time Aristotle presents a seminal perspective on abduction: the second part of the article considers the famous passage in Chapter B25 of Prior Analytics concerning ἀπαγωγή (“leading away”), also studied by Peirce. I contend that some of the current well-known distinctive characters of abductive cognition are already expressed, which are in tune with the EC-Model. By providing an illustration of the role of the method of analysis and of the middle terms in Plato's dialectic argumentation, considered as related to the diorismic/poristic process in ancient geometry – also, later on, emphasized by Proclus – I maintain that it is just this intellectual heritage which informs Aristotle' Chapter B25 on ἀπαγωγή. Even if, in general, Aristotle seems to sterilize, thanks to the invention of syllogistic theory, every “dialectic” background of reasoning, nevertheless in Chapter B25 he is still pointing to the fundamental inferential role in reasoning of those externalities that substantiate the process of “leading away” (ἀπαγωγή). Hence, we can gain a new positive perspective about the “constitutive” eco-cognitive character of abduction, just thanks to Aristotle himself. Finally, the paper presents an excursus on Aristotle's enthymemes from signs, disregarded by Peirce, but extremely important to stress the Aristotelian treatment of what I have called selective abduction. A forthcoming companion paper [35] will further deepen the EC-Model of abduction stressing stricter logical aspects: the first result will be that, contrarily to the classical logical view, relevance and plausibility in abductive reasoning have to be relativized and so the epistemologically embarrassing concepts of irrelevance and implausibility exculpated: they are not always offensive to reason. 相似文献