Incompleteness and the Halting Problem

Studia Logica - We present an abstract framework in which we give simple proofs for Gödel’s First and Second Incompleteness Theorems and obtain, as consequences, Davis’,...     

On Stage with Gunk

A structure is temporally gunky just in case all of its temporal parts have proper temporal parts. Joshua Stuchlik [2003] objects to the stage theory of persistence from temporal gunk by arguing that the former requires instantaneous entities while the latter precludes them. It is argued here that stage theory can accommodate temporal gunk by invoking short-lived persisting stages. However, a new and more serious problem for stage theory is not far to seek. The short-lived stages that are needed to accommodate gunk accord with stage theory only if they are appropriately qualitatively static. The problem is that, unless stage theory abandons much of its dialectical force, some of the required stages fail this condition. Thus, Stuchlik is right that gunk shows a large class of worlds not to be stages, but wrong about which worlds these are.     

On Logics with Coimplication

This paper investigates (modal) extensions of Heyting–Brouwer logic, i.e., the logic which results when the dual of implication (alias coimplication) is added to the language of intuitionistic logic. We first develop matrix as well as Kripke style semantics for those logics. Then, by extending the Gödel-embedding of intuitionistic logic into S4 , it is shown that all (modal) extensions of Heyting–Brouwer logic can be embedded into tense logics (with additional modal operators). An extension of the Blok–Esakia-Theorem is proved for this embedding.     

On models with variable universe

In this paper some parts of the model theory for logics based on generalised Kripke semantics are developed. Löwenheim-Skolem theorems and some applications of ultraproduct constructions for generalised Kripke models with variable universe are investigated using similar theorems of the model theory for classical logic. The results are generalizations of the theorems of [4].     

On modal logic with an intuitionistic base

A definition of the concept of Intuitionist Modal Analogue is presented and motivated through the existence of a theorem preserving translation fromMIPC (see [2]) to a bimodalS ⁴–S⁵ calculus.Allatum est die 9 Septembris 1975     

论先秦时期的以德治国思想

先秦时期国家开始形成,以德治国思想随之发轫.人性是德治的立论基点,仁政是德治的基本主张,德行是德治的伦理构架,治身是德治的个体修养,尚贤是德治的人才要求,教化是德治的重要途径.     

On Provability Logics with Linearly Ordered Modalities

We introduce the logics GLP _Λ, a generalization of Japaridze’s polymodal provability logic GLP _ω where Λ is any linearly ordered set representing a hierarchy of provability operators of increasing strength. We shall provide a reduction of these logics to GLP _ω yielding among other things a finitary proof of the normal form theorem for the variable-free fragment of GLP _Λ and the decidability of GLP _Λ for recursive orderings Λ. Further, we give a restricted axiomatization of the variable-free fragment of GLP _Λ.     

On Endomorphisms of Ockham Algebras with Pseudocomplementation

A pO-algebra ${(L; f, \, ^{\star})}$ is an algebra in which (L; f) is an Ockham algebra, ${(L; \, ^{\star})}$ is a p-algebra, and the unary operations f and ${^{\star}}$ commute. Here we consider the endomorphism monoid of such an algebra. If ${(L; f, \, ^{\star})}$ is a subdirectly irreducible pK _1,1- algebra then every endomorphism ${\vartheta}$ is a monomorphism or ${\vartheta^3 = \vartheta}$ . When L is finite the endomorphism monoid of L is regular, and we determine precisely when it is a Clifford monoid.     

On the Possibility of Presentism with Occurrents

Philosophia - This paper defends the possibility of admitting occurrents in a presentist ontology. Two ways of doing so are proposed, the first one involves Meinongian presentism. By using the...     

On Polarizing Outranking Relations with Large Performance Differences

We introduce a bipolarly extended veto principle—a positive, as well as negative, large performance differences polarization—which allows us to extend the definition of the classical outranking relation in such a way that the identity between its asymmetric part and its codual relation is preserved. Copyright © 2012 John Wiley & Sons, Ltd.     

On Conservative Extensions in Logics with Infinitary Predicates

If the language is extended by new individual variables, in classical first order logic, then the deduction system obtained is a conservative extension of the original one. This fails to be true for the logics with infinitary predicates. But it is shown that restricting the commutativity of quantifiers and the equality axioms in the extended system and supposing the merry-go-round property in the original system, the foregoing extension is already conservative. It is shown that these restrictions are crucial for an extension to be conservative. The origin of the results is algebraic logic. Presented by Daniele Mundici Supported by grant OTKA T43242.     

Bring It On: Proactive Coping with Discrimination

We investigated proactive coping with discrimination among heavy women in both a high impact lab study (101 women) and a daily diary study (62 women). Heavy women assessed greater harm and fewer coping resources for discriminatory, as compared to non-discriminatory, hassles (Study 2). Primary appraisals of harm were important determinants of proactive coping, including primary control (attempts to change the environment) and secondary control (attempts to change the self to fit the environment) directed at discriminatory stressors (Studies 1 and 2). When heavy women used primary control coping efforts, they experienced positive interpersonal outcomes (Study 1) and less negative intrapersonal outcomes (Study 2). We discuss the benefits and limitations of engaging in proactive coping and suggest avenues for future research.