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 \(\mathsf{GLK}\).     

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...     

$$\mathrm {ZF}$$ 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...     

Types of \mathsf{I} -Free Hereditary Right Maximal Terms

The implicational fragment of the relevance logic “ticket entailment” is closely related to the so-called hereditary right maximal terms. I prove that the terms that need to be considered as inhabitants of the types which are theorems of T_→ are in normal form and built in all but one case from and only. As a tool in the proof ordered term rewriting systems are introduced. Based on the main theorem I define FIT_→ – a Fitch-style calculus (related to FT_→) for the implicational fragment of ticket entailment.     

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 $${...     

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.     

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...     

$${\in_K}$$: a Non-Fregean Logic of Explicit Knowledge

We present a new logic-based approach to the reasoning about knowledge which is independent of possible worlds semantics. \({\in_K}\) (Epsilon-K) is a non-Fregean logic whose models consist of propositional universes with subsets for true, false and known propositions. Knowledge is, in general, not closed under rules of inference; the only valid epistemic principles are the knowledge axiom K _i φ → φ and some minimal conditions concerning common knowledge in a group. Knowledge is explicit and all forms of the logical omniscience problem are avoided. Various stronger epistemic properties such as positive and/or negative introspection, the K-axiom, closure under logical connectives, etc. can be restored by imposing additional semantic constraints. This yields corresponding sublogics for which we present sound and complete axiomatizations. As a useful tool for general model constructions we study abstract versions of some 3-valued logics in which we interpret truth as knowledge. We establish a connection between \({\in_K}\) and the well-known syntactic approach to explicit knowledge proving a result concerning equi-expressiveness. Furthermore, we discuss some self-referential epistemic statements, such as the knower paradox, as relaxations of variants of the liar paradox and show how these epistemic “paradoxes” can be solved in \({\in_K}\). Every specific \({\in_K}\)-logic is defined as a certain extension of some underlying classical abstract logic.     

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...     

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.     

中国逻辑学会形式逻辑专业委员会2003年学术研讨会概述

由中国逻辑学会形式逻辑专业委员会主办、绵阳师范学院承办的逻辑学术研讨会于2003年12月13～15日在四川绵阳市举行,来自全国数十所高校和科研机构的专家学者出席了研讨会.与会者讨论了逻辑学的国际前沿动态、现代逻辑的发展及与相邻学科的交叉研究、语言逻辑的研究阶段和途径等学术问题.大会特别针对高等教育中非形式逻辑教学和批判性思维的学科理念、课程框架等热点问题进行了广泛热烈的探讨.     

The Weak Normalization of the Simply Typed {lambda}se-calculus

In this paper, we show the weak normalization (WN) of the simply-typeds_e-calculus with open terms where abstractions are decoratedwith types, and metavariables, de Bruijn indices and updatingoperators are decorated with environments. We show a proof ofWN using the _e-calculus, a calculus isomorphic to . This proof is strongly influenced by Goubault-Larrecq'sproof of WN for the -calculus but with subtle differences whichshow that the two styles require different attention. Furthermore,we give a new calculus '_e which works like s_e but which iscloser to than _e. For both _e and '_e we prove WN for typedsemi-open terms (i.e. those which allow term variables but nosubstitution variables), unlike the result of Goubault-Larrecqwhich covered all open terms.     

An Axiomatic System and a Tableau Calculus for STIT Imagination Logic

We formulate a Hilbert-style axiomatic system and a tableau calculus for the STIT-based logic of imagination recently proposed in Wansing (2015). Completeness of the axiom system is shown by the method of canonical models; completeness of the tableau system is also shown by using standard methods.