Logics for Moderate Belief-Disagreement Between Agents

Studia Logica - A moderate belief-disagreement between agents on proposition p means that one agent believes p and the other agent does not. This paper presents two logical systems, $$\mathbf...     

Game Logic is Strong Enough for Parity Games

We investigate the expressive power of Parikh's Game Logic interpreted in Kripke structures, and show that the syntactical alternation hierarchy of this logic is strict. This is done by encoding the winning condition for parity games of rank n. It follows that Game Logic is not captured by any finite level of the modal -calculus alternation hierarchy. Moreover, we can conclude that model checking for the -calculus is efficiently solvable iff this is possible for Game Logic     

Semi-intuitionistic Logic with Strong Negation

Motivated by the definition of semi-Nelson algebras, a propositional calculus called semi-intuitionistic logic with strong negation is introduced and proved to be complete with respect to that class of algebras. An axiomatic extension is proved to have as algebraic semantics the class of Nelson algebras.     

Constructive Logic with Strong Negation is a Substructural Logic. I

The goal of this two-part series of papers is to show that constructive logic with strong negation N is definitionally equivalent to a certain axiomatic extension NFL _ew of the substructural logic FL _ew . In this paper, it is shown that the equivalent variety semantics of N (namely, the variety of Nelson algebras) and the equivalent variety semantics of NFL _ew (namely, a certain variety of FL _ew -algebras) are term equivalent. This answers a longstanding question of Nelson [30]. Extensive use is made of the automated theorem-prover Prover9 in order to establish the result. The main result of this paper is exploited in Part II of this series [40] to show that the deductive systems N and NFL _ew are definitionally equivalent, and hence that constructive logic with strong negation is a substructural logic over FL _ew . Presented by Heinrich Wansing     

Constructive Logic with Strong Negation is a Substructural Logic. II

The goal of this two-part series of papers is to show that constructive logic with strong negation N is definitionally equivalent to a certain axiomatic extension NFL _ew of the substructural logic FL _ew . The main result of Part I of this series [41] shows that the equivalent variety semantics of N (namely, the variety of Nelson algebras) and the equivalent variety semantics of NFL _ew (namely, a certain variety of FL _ew -algebras) are term equivalent. In this paper, the term equivalence result of Part I [41] is lifted to the setting of deductive systems to establish the definitional equivalence of the logics N and NFL _ew . It follows from the definitional equivalence of these systems that constructive logic with strong negation is a substructural logic. Presented by Heinrich Wansing     

Computing Strong and Weak Permissions in Defeasible Logic

In this paper we propose an extension of Defeasible Logic to represent and compute different concepts of defeasible permission. In particular, we discuss some types of explicit permissive norms that work as exceptions to opposite obligations or encode permissive rights. Moreover, we show how strong permissions can be represented both with, and without introducing a new consequence relation for inferring conclusions from explicit permissive norms. Finally, we illustrate how a preference operator applicable to contrary-to-duty obligations can be combined with a new operator representing ordered sequences of strong permissions. The logical system is studied from a computational standpoint and is shown to have linear computational complexity.     

On All Strong Kleene Generalizations of Classical Logic

By using the notions of exact truth (‘true and not false’) and exact falsity (‘false and not true’), one can give 16 distinct definitions of classical consequence. This paper studies the class of relations that results from these definitions in settings that are paracomplete, paraconsistent or both and that are governed by the (extended) Strong Kleene schema. Besides familiar logics such as Strong Kleene logic (K3), the Logic of Paradox (LP) and First Degree Entailment (FDE), the resulting class of all Strong Kleene generalizations of classical logic also contains a host of unfamiliar logics. We first study the members of our class semantically, after which we present a uniform sequent calculus (the SK calculus) that is sound and complete with respect to all of them. Two further sequent calculi (the \({{\bf SK}^\mathcal{P}}\) and \({\bf SK}^{\mathcal{N}}\) calculus) will be considered, which serve the same purpose and which are obtained by applying general methods (due to Baaz et al.) to construct sequent calculi for many-valued logics. Rules and proofs in the SK calculus are much simpler and shorter than those of the \({\bf SK}^{\mathcal{P}}\) and the \({\bf SK}^{\mathcal{N}}\) calculus, which is one of the reasons to prefer the SK calculus over the latter two. Besides favourably comparing the SK calculus to both the \({\bf SK}^{\mathcal{P}}\) and the \({\bf SK}^{\mathcal{N}}\) calculus, we also hint at its philosophical significance.     

Quantized Linear Logic,Involutive Quantales and Strong Negation

A new logic, quantized intuitionistic linear logic (QILL), is introduced, and is closely related to the logic which corresponds to Mulvey and Pelletier's (commutative) involutive quantales. Some cut-free sequent calculi with a new property quantization principle and some complete semantics such as an involutive quantale model and a quantale model are obtained for QILL. The relationship between QILL and Wansing's extended intuitionistic linear logic with strong negation is also observed using such syntactical and semantical frameworks.     

Associations Between Participant Ratings of PREP for Strong Bonds and Marital Outcomes 1 Year Postintervention

After completing a relationship education program, collecting participant evaluations of the program is common practice. These are generally used as an index of “consumer satisfaction” with the program, with implications for feasibility and quality. Rarely have these ratings been used as predictors of changes in marital quality, although such feedback may be the only data providers collect or have immediate access to when considering the success of their efforts. To better understand the utility of such ratings to predict outcomes, we evaluated links between participant ratings and changes in self-reported marital satisfaction and communication scores 1 year later for a sample of 191 Army couples who had participated in a relationship education program delivered by Army chaplains (PREP for Strong Bonds). Overall ratings of general satisfaction with the program and the leader did not predict changes in marital outcomes 1 year later, whereas higher ratings of how much was learned, program helpfulness, increased similarity in outlook regarding Army life, and helpfulness of communication skills training predicted greater change in communication skills 1 year later. Higher ratings of items reflecting intent to invest more time in the relationship, and increased confidence in constructive communication and working as a team with the spouse predicted greater increases in both marital satisfaction and communication skills 1 year later. The constructs of intention and confidence (akin to perceived behavioral control) suggest that the Theory of Planned Behavior may be particularly useful when considering which Army couples will show ongoing benefit after relationship education.     

推理心理研究中的逻辑加工与非逻辑加工评析

本文对西方心理学研究中有关推理心理学争论的两个热点问题之一：逻辑推理与非逻辑推理之争的发展线索和相互关系等问题进行了评述,指出了这两种理论争论中未能注意到的三个问题,并对试图解决这三个问题的“知识和试题双重结构模型”作了简要介绍。     

Describing categories of objects for menu retrieval systems

When searching for information in menu-based retrieval systems, users are given a choice among a set of categories. Successful retrieval of information depends critically on the user’s understanding the system’s division of objects into categories and the system’s labels for these categories. This research compares several different ways of describing ill-defined categories of objects using combinations of names and examples. Examples provide a promising possibility, both as a means of flexibly naming new or difficult menu categories and as a methodological tool for studying certain categorization problems.     

A Common Framework for Describing Some Outranking Methods

Outranking methods such as ELECTRE have been proposed for aggregating preference information on several criteria into an overall preference structure in cases where the multiattribute utility approach is not appropriate or feasible. We present here a framework in which such methods may be described and, hopefully in the future, axiomatically characterized. We point out several characteristics such as independence and semiordinality which seem to be pertinent to delineate the field of application of these procedures. © 1997 John Wiley & Sons, Ltd.     

三个历史决议与站起来、富起来、强起来的逻辑理路

中国共产党先后形成的三个关于历史问题的决议,与站起来、富起来到强起来,与实现中华民族伟大复兴有着非常密切的关系。前两个历史决议主要总结党的历史的教训、分清历史是非,在此基础上胜利前进。第三个历史决议主要总结党的百年奋斗重大成就和历史经验,重点总结新时代党和国家事业取得的历史性成就、发生的历史性变革和积累的新鲜经验,在此基础上激励在新时代新征程上夺取新的更加伟大的胜利。三个历史决议都形成于重大历史关头,都是向历史问计,都努力从历史中汲取智慧和力量,都达到或必将达到更好服务现实的预期目的和效果。     

Logic,Logic, and Logic

In his recent paper in History and Philosophy of Logic, John Kearns argues for a solution of the Liar paradox using an illocutionary logic (Kearns 2007 Kearns, J. 2007. ‘An illocutionary logical explanation of the Liar Paradox’. History and Philosophy of Logic, 28: 31–66. [Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]). Paraconsistent approaches, especially dialetheism, which accepts the Liar as being both true and false, are rejected by Kearns as making no ‘clear sense’ (p. 51). In this critical note, I want to highlight some shortcomings of Kearns' approach that concern a general difficulty for supposed solutions to (semantic) antinomies like the Liar. It is not controversial that there are languages which avoid the Liar. For example, the language which consists of the single sentence ‘Benedict XVI was born in Germany’ lacks the resources to talk about semantics at all and thus avoids the Liar. Similarly, more interesting languages such as the propositional calculus avoid the Liar by lacking the power to express semantic concepts or to quantify over propositions. Kearns also agrees with the dialetheist claim that natural languages are semantically closed (i.e. are able to talk about their sentences and the semantic concepts and distinctions they employ). Without semantic closure, the Liar would be no real problem for us (speakers of natural languages). But given the claim, the expressive power of natural languages may lead to the semantic antinomies. The dialetheist argues for his position by proposing a general hypothesis (cf. Bremer 2005 Bremer, M. 2005. An Introduction to Paraconsistent Logics, Bern: Lang.  [Google Scholar], pp. 27–28): ‘(Dilemma) A linguistic framework that solves some antinomies and is able to express its linguistic resources is confronted with strengthened versions of the antinomies’. Thus, the dialetheist claims that either some semantic concepts used in a supposed solution to a semantic antinomy are inexpressible in the framework used (and so, in view of the claim, violate the aim of being a model of natural language), or else old antinomies are exchanged for new ones. One horn of the dilemma is having inexpressible semantic properties. The other is having strengthened versions of the antinomies, once all semantic properties used are expressible. This dilemma applies, I claim, to Kearns' approach as well.