Gentzen-Style Axiomatizations for Some Conservative Extensions of Basic Propositional Logic

We introduce two Gentzen-style sequent calculus axiomatizations for conservative extensions of basic propositional logic. Our first axiomatization is an ipmrovement of, in the sense that it has a kind of the subformula property and is a slight modification of. In this system the cut rule is eliminated. The second axiomatization is a classical conservative extension of basic propositional logic. Using these axiomatizations, we prove interpolation theorems for basic propositional logic.     

A Translation of Intuitionistic Predicate Logic into Basic Predicate Logic

Basic Predicate Logic, BQC, is a proper subsystem of Intuitionistic Predicate Logic, IQC. For every formula in the language {, , , , , , }, we associate two sequences of formulas 0,1,... and 0,1,... in the same language. We prove that for every sequent , there are natural numbers m, n, such that IQC , iff BQC n m. Some applications of this translation are mentioned.     

An overview of algorithmic approaches to compute optimum entropy distributions in the expert system shell MECore (extended version)

The expert system shell MECore provides a series of knowledge management operations to define probabilistic knowledge bases and to reason under uncertainty. To provide a reference work for MECore algorithmics, we bring together results from different sources that have been applied in MECore and explain their intuitive ideas. Additionally, we report on our ongoing work regarding further development of MECore's algorithms to compute optimum entropy distributions and provide some empirical results. Altogether this paper explains the intuition of important theoretical results and their practical implications, compares old and new algorithmic approaches and points out their benefits as well as possible limitations and pitfalls.     

Mistaking the instance for the rule: A critical analysis of the truth-table evaluation paradigm

Many studies probe for interpretations of < if A then C> by having people evaluate truth-table cases (<A and C>, < A and not-C>, < not-A and C>, < not-A and not-C>) as making the rule true or false, or being irrelevant. We argue that a single case can never prove a general rule to be true, as philosophy of science has taught any researcher. Giving participants the impossible “true” option would therefore bias results away from this response. In Experiment 1 people judged instead whether cases make a rule false, do not make the rule false, or are irrelevant to the rule. The experimental group (N = 44) showed a significant increase in not-false responses compared with true responses of the control group (N = 39). In Experiments 2 and 3 the experimental groups judged whether cases make a rule true, corroborate it (i.e., make the rule more plausible, but neither true nor false), make it false, or are irrelevant. There was a significant reduction of irrelevant responses as compared to the default true/false/irrelevant task for the control groups. Even < A and C> cases were often no longer considered to make an < if A then C> rule true and were correctly judged to corroborate (vs. verify) rules. Results corroborate our conceptual analyses of the unsuitable “true” response option and put into question arguments that hinge on the presumed likelihood by which people consider truth contingencies to make a rule “true”.     

When family considerations influence work decisions: Decision-making processes

The work–family literature has provided an abundance of evidence that various family factors are linked to various work decisions, suggesting that the “family-relatedness” of work decisions is a prevalent phenomenon (Greenhaus & Powell, 2012). However, the cognitive processes by which such linkages occur have received little attention. We offer a framework by which to examine individuals' decision-making processes when they take family considerations into account in their work decisions. The framework suggests stages through which individuals proceed when making a work decision that takes family considerations into account and cognitive processes that influence how they proceed through each stage.     

How is God-talk logically possible? A sketch for an argument on the logic of ‘God’

In this paper I want to argue for the optimal way to characterise the logical and semantical behaviour of the singular term ‘God’ used in religious language. The relevance of this enterprise to logical theory is the main focus as well. Doing this presupposes to outline the two rivaling approaches of well-definition of singular terms: Kripke’s (“rigid designators”) and Hintikka’s (“world-lines”). ‘God’ as a “rigid designator” is purified from all real-life-language-games of identification and only spells out a metaphysical tag, which favours the view of “anything goes”. Instead, ‘God’ as a “world-line,” plus two ways of quantification, is much more flexible to theological traditions, teachings of the church, religious practices and personal feelings. Thus, it provides a sufficiently well-defined singular term for the purposes of logical theory. The whole sketch is based on Jaakko Hintikka’s logical ideas, mainly on his responses to different authors in PJH. I have systematically omitted direct references to his texts because I have modified considerably his ideas for my own purposes.     

现象学与逻辑学

无论在胡塞尔思想中还是在海德格尔思想中,现象学与逻辑学的关系都构成一个核心问题。本文首先再现了胡塞尔前后期在此问题上的相关研究,并指出他的超越论逻辑学的要点在于对本质的前逻辑直观,也是最有可能为逻辑学提供哲学支撑的因素。其次,在海德格尔方面,根据律概念成为讨论现象学与逻辑学关系的切入点,由此导出他的“存在理解”、“无蔽”和“自由”的概念解释。他们的共同点在于：把形式逻辑看作陈述逻辑,并试图用前谓词判断的哲学逻辑学来为它奠基。