Arithmetical Soundness and Completeness for $$\varvec{\Sigma }_{\varvec{2}}$$ Numerations

We prove that for each recursively axiomatized consistent extension T of Peano Arithmetic and \(n \ge 2\), there exists a \(\Sigma _2\) numeration \(\tau (u)\) of T such that the provability logic of the provability predicate \(\mathsf{Pr}_\tau (x)\) naturally constructed from \(\tau (u)\) is exactly \(\mathsf{K}+ \Box (\Box ^n p \rightarrow p) \rightarrow \Box p\). This settles Sacchetti’s problem affirmatively.     

Categorical Equivalence Between $$\varvec{PMV}_{\varvec{f}}$$ PMV f -Product Algebras and Semi-Low $$\varvec{f}_{\varvec{u}}$$ f u -Rings

Studia Logica - An explicit categorical equivalence is defined between a proper subvariety of the class of $${ PMV}$$ -algebras, as defined by Di Nola and Dvure?enskij, to be called $${...     

Analyticity,Balance and Non-admissibility of $$\varvec{Cut}$$ Cut in Stoic Logic

Studia Logica - This paper shows that, for the Hertz–Gentzen Systems of 1933 (without Thinning), extended by a classical rule T1 (from the Stoics) and using certain axioms (also from the...     

An Abductive Question-Answer System for the Minimal Logic of Formal Inconsistency $$\mathsf {mbC}$$ mbC

Studia Logica - The aim in this paper is to define an Abductive Question-Answer System for the minimal logic of formal inconsistency $$\mathsf {mbC}$$ . As a proof-theoretical basis we employ the...     

Estimating the Cognitive Diagnosis $$\varvec{Q}$$ Q Matrix with Expert Knowledge: Application to the Fraction-Subtraction Dataset

Psychometrika - Cognitive diagnosis models (CDMs) are an important psychometric framework for classifying students in terms of attribute and/or skill mastery. The $$\varvec{Q}$$ matrix, which...     

Arithmetical Completeness Theorem for Modal Logic $$\mathsf{}$$

We prove that for any recursively axiomatized consistent extension T of Peano Arithmetic, there exists a \(\Sigma _2\) provability predicate of T whose provability logic is precisely the modal logic \(\mathsf{K}\). For this purpose, we introduce a new bimodal logic \(\mathsf{GLK}\), and prove the Kripke completeness theorem and the uniform arithmetical completeness theorem for \(\mathsf{GLK}\).     

$$\mathrm {ZF}$$ ZF Between Classicality and Non-classicality

Studia Logica - We present a generalization of the algebra-valued models of $$\mathrm {ZF}$$ where the axioms of set theory are not necessarily mapped to the top element of an algebra, but may get...     

Explicit Fixed Points in Interpretability Logic

The problem of Uniqueness and Explicit Definability of Fixed Points for Interpretability Logic is considered. It turns out that Uniqueness is an immediate corollary of a theorem of Smoryski.     

Two Maximality Results for the Lattice of Extensions of $$\vdash _{\mathbf {RM}}$$

Studia Logica - We use an algebraic argument to prove that there are exactly two premaximal extensions of $$\mathbf {RM}$$ ’s consequence. We also show that one of these extensions is the...     

The Logic of Knowledge Based Obligation

Deontic Logic goes back to Ernst Mally’s 1926 work, Grundgesetze des Sollens: Elemente der Logik des Willens [Mally. E.: 1926, Grundgesetze des Sollens: Elemente der Logik des Willens, Leuschner & Lubensky, Graz], where he presented axioms for the notion ‘p ought to be the case’. Some difficulties were found in Mally’s axioms, and the field has much developed. Logic of Knowledge goes back to Hintikka’s work Knowledge and Belief [Hintikka, J.: 1962, Knowledge and Belief: An Introduction to the Logic of the Two Notions, Cornell University Press] in which he proposed formal logics of knowledge and belief. This field has also developed quite a great deal and is now the subject of the TARK conferences. However, there has been relatively little work combining the two notions of knowledge (belief) with the notion of obligation. (See, however, [Lomuscio, A. and Sergot, M.: 2003, Studia Logica 75 63–92; Moore, R. C.: 1990, In J. F. Allen, J. Hendler and A. Tate (eds.), Readings in Planning, Morgan Kaufmann Publishers, San Mateo, CA]) In this paper we point out that an agent’s obligations are often dependent on what the agent knows, and indeed one cannot reasonably be expected to respond to a problem if one is not aware of its existence. For instance, a doctor cannot be expected to treat a patient unless she is aware of the fact that he is sick, and this creates a secondary obligation on the patient or someone else to inform the doctor of his situation. In other words, many obligations are situation dependent, and only apply in the presence of the relevant information. Thus a case for combining Deontic Logic with the Logic of Knowledge is clear. We introduce the notion of knowledge based obligation and offer an S5, history based Kripke semantics to express this notion, as this semantics enables us to represent how information is transmitted among agents and how knowledge changes over time as a result of communications. We consider both the case of an absolute obligation (although dependent on information) as well as the (defeasible) notion of an obligation which may be over-ridden by more relevant information. For instance a physician who is about to inject a patient with drug d may find out that the patient is allergic to d and that she should use d′ instead. Dealing with the second kind of case requires a resort to non-monotonic reasoning and the notion of justified belief which is stronger than plain belief, but weaker than absolute knowledge in that it can be over-ridden. This notion of justified belief also creates a derived notion of default obligation where an agent has, as far as the agent knows, an obligation to do some action a. A dramatic application of this notion is our analysis of the Kitty Genovese case where, in 1964, a young woman was stabbed to death while 38 neighbours watched from their windows but did nothing. The reason was not indifference, but none of the neighbours had even a default obligation to act, even though, as a group, they did have an obligation to take some action to protect Kitty. Earlier versions of this paper were presented at the conferences SEP-2004, and DALT-2004.     

Philosophy of Science: Interfaces between Logic and Knowledge Representation

Abstract

In this inaugural lecture I offer, against the background of a discussion of knowledge representation and its tools, an overview of my research in the philosophy of science. I defend a relational model-theoretic realism as being the appropriate meta-stance most congruent with the model-theoretic view of science as a form of human engagement with the world. Making use of logics with preferential semantics within a model-theoretic paradigm, I give an account of science as process and product. I demonstrate the power of the full-blown employment of this paradigm in the philosophy of science by discussing the main applications of model-theoretic realism to traditional problems in the philosophy of science.

I discuss my views of the nature of logic and of its role in the philosophy of science today. I also specifically offer a brief discussion on the future of cognitive philosophy in South Africa. My conclusion is a general look at the nature of philosophical inquiry and its significance for philosophers today.     

Logic of Knowledge and Utterance and the Liar

We extend the ordinary logic of knowledge based on the operator K and the system of axioms S₅ by adding a new operator U, standing for the agent utters , and certain axioms and a rule for U, forming thus a new system KU. The main advantage of KU is that we can express in it intentions of the speaker concerning the truth or falsehood of the claims he utters and analyze them logically. Specifically we can express in the new language various notions of lying, as well as of telling the truth. Consequently, as long as lying or telling the truth about a fact is an intentional mode of the speaker, we can resolve the Liar paradox, or at least some of its variants, turning it into an ordinary (false or true) sentence. Also, using Kripke structures analogous to those employed by S. Kraus and D. Lehmann in [3] for modelling the logic of knowledge and belief, we offer a sound and complete semantics for KU.     

外显知识对运动技能内隐学习的影响

总结了近年来关于外显知识对运动技能内隐学习影响的研究。提出外显知识对内隐学习存在影响,但其作用的大小及其性质取决于外显知识的呈现时间、内容、内隐规则的可觉察程度、认知负荷以及压力等因素。提供外显知识既可能有利于任务的完成,也可能激发与任务规则无关的注意过程,阻碍内隐学习。外显知识可影响行为,却不一定能被有意识地提取。外显知识对学习者的认知过程和动作模式均会产生影响。     

Epistemic Friction: Reflections on Knowledge, Truth, and Logic

Knowledge requires both freedom and friction. Freedom to set up our epistemic goals, choose the subject matter of our investigations, espouse cognitive norms, design research programs, etc., and friction (constraint) coming from two directions: the object or target of our investigation, i.e., the world in a broad sense, and our mind as the sum total of constraints involving the knower. My goal is to investigate the problem of epistemic friction, the relation between epistemic friction and freedom, the viability of foundationalism as a solution to the problem of friction, an alternative solution in the form of a neo-Quinean model, and the possibility of solving the problem of friction as it applies to logic and the philosophy of logic within that model.     

Motivation Among Pre-intermediate Iranian Language Learners: From Explicit Knowledge Toward Implicit Syntactic Development

The variable success in learning a second language (L2) may be best explained by varying degrees of motivation. This study investigated whether individual differences in appraisal dimensions of motivation explained explicit and implicit syntactic knowledge. Participants learned three syntactic structures under implicit and explicit training conditions. They also completed two motivation questionnaires before instruction. Syntactic development was assessed at early and late stages of acquisition. Results indicated superior performance on the tests of explicit knowledge, but a limited effect for the role of motivation in its development. However, with improvement in implicit knowledge at delayed testing, positive relationships emerged with several motivational dimensions. The results support L2 theoretical perspectives that posit different roles for explicit and implicit knowledge at early and late stages of L2 grammar, respectively. The findings also indicate that variation in learners’ patterns of stimulus appraisals may contribute to variable success in the development of implicit knowledge.     

There are2^{\aleph _0 } logics with the relevance principle betweenR andRM

The aim of the paper is to prove the result announced by the title.     

Latent Variable Selection for Multidimensional Item Response Theory Models via $$L_{1}$$ Regularization

We develop a latent variable selection method for multidimensional item response theory models. The proposed method identifies latent traits probed by items of a multidimensional test. Its basic strategy is to impose an \(L_{1}\) penalty term to the log-likelihood. The computation is carried out by the expectation–maximization algorithm combined with the coordinate descent algorithm. Simulation studies show that the resulting estimator provides an effective way in correctly identifying the latent structures. The method is applied to a real dataset involving the Eysenck Personality Questionnaire.