Dynamic Deontic Logic and its Paradoxes

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     

A new formulation of the Principle of Indifference

The idea of a probabilistic logic of inductive inference based on some form of the principle of indifference has always retained a powerful appeal. However, up to now all modifications of the principle failed. In this paper, a new formulation of such a principle is provided that avoids generating paradoxes and inconsistencies. Because of these results, the thesis that probabilities cannot be logical quantities, determined in an objective way through some form of the principle of indifference, is no longer supportable. Later, the paper investigates some implications of the new principle of indifference. To conclude, a re-examination of the foundations of the so-called objective Bayesian inference is called for.     

The Craig Interpolation Theorem in abstract model theory

The Craig Interpolation Theorem is intimately connected with the emergence of abstract logic and continues to be the driving force of the field. I will argue in this paper that the interpolation property is an important litmus test in abstract model theory for identifying “natural,” robust extensions of first order logic. My argument is supported by the observation that logics which satisfy the interpolation property usually also satisfy a Lindström type maximality theorem. Admittedly, the range of such logics is small.     

Quantified coalition logic

We add a limited but useful form of quantification to Coalition Logic, a popular formalism for reasoning about cooperation in game-like multi-agent systems. The basic constructs of Quantified Coalition Logic (QCL) allow us to express such properties as “every coalition satisfying property P can achieve φ” and “there exists a coalition C satisfying property P such that C can achieve φ”. We give an axiomatisation of QCL, and show that while it is no more expressive than Coalition Logic, it is nevertheless exponentially more succinct. The complexity of QCL model checking for symbolic and explicit state representations is shown to be no worse than that of Coalition Logic, and satisfiability for QCL is shown to be no worse than satisfiability for Coalition Logic. We illustrate the formalism by showing how to succinctly specify such social choice mechanisms as majority voting, which in Coalition Logic require specifications that are exponentially long in the number of agents.     

论推类逻辑与中国古代医学

推类逻辑就是基于“推类”的中国古代逻辑。易数推类为中医科学提供了一个有效工具,提供了一个有效地认识自然、机体（肌体）、疾病的方法。取象比类是中医思维的核心,推类是中国古代医学辨证论治的基本方法。推类具有很强的具象性,并以比类为基础。     

Which should you use,intuition or logic? Cultural differences in injunctive norms about reasoning

Past research has shown that tendencies to engage in holistic and analytical reasoning are differentially encouraged by East Asian and Western cultures. But little is known about cultural differences in the perceived value of analytic versus intuitive reasoning. In Study 1, Koreans and Americans ranked the importance of traits including ‘intuitive’ and ‘logical’ in work and family contexts. In Study 2, Euro‐Canadians and East‐Asian‐Canadians read scenarios of intuitive versus rule‐following business decisions. Relative to Western participants, East Asians rated intuitive reasoning as more important and reasonable than analytic reasoning. Implications for the epistemic status of reasoning modes, culture's effect on values about reasoning, and multiculturalism are discussed.     

The seven virtues of simple type theory

Simple type theory, also known as higher-order logic, is a natural extension of first-order logic which is simple, elegant, highly expressive, and practical. This paper surveys the virtues of simple type theory and attempts to show that simple type theory is an attractive alternative to first-order logic for practical-minded scientists, engineers, and mathematicians. It recommends that simple type theory be incorporated into introductory logic courses offered by mathematics departments and into the undergraduate curricula for computer science and software engineering students.     

Living up to one's commitments: Agency, strategies and trust

In human social interaction, the notions of commitment and trust are strongly interrelated. A formal model for this interrelation will enable artificial agents to benefit from the associated reduction of complexity and improved possibilities for cooperation. We argue that the notion of living up to one's commitments, rather than actual fulfillment, plays the key role in the trust–commitment interrelation, and we propose a formal analysis of that notion in the framework of agents and strategies in branching time. The main technical innovation is a stringency ordering on an agent's strategies that allows one to classify what an agent does as more or less appropriate with respect to a given commitment, leading to a fine-grained assessment of trustworthiness.     

On Permutation in Simplified Semantics

This note explains an error in Restall’s ‘Simplified Semantics for Relevant Logics (and some of their rivals)’ (Restall, J Philos Logic 22(5):481–511, 1993) concerning the modelling conditions for the axioms of assertion A → ((A → B) → B) (there called c6) and permutation (A → (B → C)) → (B → (A → C)) (there called c7). We show that the modelling conditions for assertion and permutation proposed in ‘Simplified Semantics’ overgenerate. In fact, they overgenerate so badly that the proposed semantics for the relevant logic R validate the rule of disjunctive syllogism. The semantics provides for no models of R in which the “base point” is inconsistent. This problem is not restricted to ‘Simplified Semantics.’ The techniques of that paper are used in Graham Priest’s textbook An Introduction to Non-Classical Logic (Priest, 2001), which is in wide circulation: it is important to find a solution. In this article, we explain this result, diagnose the mistake in ‘Simplified Semantics’ and propose two different corrections.     

Weakly higher order cylindric algebras and finite axiomatization of the representables

We show that the variety of n-dimensional weakly higher order cylindric algebras, introduced in Németi [9], [8], is finitely axiomatizable when n > 2. Our result implies that in certain non-well-founded set theories the finitization problem of algebraic logic admits a positive solution; and it shows that this variety is a good candidate for being the cylindric algebra theoretic counterpart of Tarski’s quasi-projective relation algebras. Supported by the Hungarian National Foundation for Scientific Research grant T73601.