A theory-based epistemology of modality

We have some justified beliefs about modal matters. A modal epistemology should explain what’s involved in our having that justification. Given that we’re realists about modality, how should we expect that explanation to go? In the first part of this essay, I suggest an answer to this question based on an analogy with games. Then, I outline a modal epistemology that fits with that answer. According to a theory-based epistemology of modality, you justifiably believe that p if (a) you justifiably believe a theory that says that p and (b) you believe p on the basis of that theory.     

Genuine Violations of Laws

Could laws of nature be violated, in the sense that some proposition is both a law and false? I argue that opponents of regularity theories of laws should accept the metaphysical possibility of such genuine violations. I begin with a clarification of this claim. The main argument is then developed in three steps. I first argue that opponents of regularity theory should endorse the modal-essence view: certain modal principles are essential to the laws of nature. Second, I argue that the modal-essence view entails sophisticated modal primitivism. Third, I argue from sophisticated primitivism to the metaphysical possibility of genuine violations of laws.     

A Calculus of Substitutions for DPL

We consider substitutions in order sensitive situations, having in the back of our minds the case of dynamic predicate logic (DPL) with a stack semantics. We start from the semantic intuition that substitutions are move instructions on stacks: the syntactic operation [y/x] is matched by the instruction to move the value of the y-stack to the x-stack. We can describe these actions in the positive fragment of DPLE. Hence this fragment counts as a logic for DPL-substitutions. We give a calculus for the fragment and prove soundness and completeness.     

Distributed Knowability and Fitch’s Paradox

Recently predominant forms of anti-realism claim that all truths are knowable. We argue that in a logical explanation of the notion of knowability more attention should be paid to its epistemic part. Especially very useful in such explanation are notions of group knowledge. In this paper we examine mainly the notion of distributed knowability and show its effectiveness in the case of Fitch’s paradox. Proposed approach raised some philosophical questions to which we try to find responses. We also show how we can combine our point of view on Fitch’s paradox with the others. Next we give an answer to the question: is distributed knowability factive? At the end, we present some details concerning a construction of anti-realist modal epistemic logic.     

Notes on Logics of Metric Spaces

In [14], we studied the computational behaviour of various first-order and modal languages interpreted in metric or weaker distance spaces. [13] gave an axiomatisation of an expressive and decidable metric logic. The main result of this paper is in showing that the technique of representing metric spaces by means of Kripke frames can be extended to cover the modal (hybrid) language that is expressively complete over metric spaces for the (undecidable) two-variable fragment of first-order logic with binary pred-icates interpreting the metric. The frame conditions needed correspond rather directly with a Boolean modal logic that is, again, of the same expressivity as the two-variable fragment. We use this representation to derive an axiomatisation of the modal hybrid variant of the two-variable fragment, discuss the compactness property in distance logics, and derive some results on (the failure of) interpolation in distance logics of various expressive power. Presented by Melvin Fitting     

A Duality for the Algebras of a Łukasiewicz <Emphasis Type="Italic">n</Emphasis> + 1-valued Modal System

In this paper, we develop a duality for the varieties of a Łukasiewicz n + 1-valued modal system. This duality is an extension of Stone duality for modal algebras. Some logical consequences (such as completeness results, correspondence theory...) are then derived and we propose some ideas for future research. Presented by Daniele Mundici     

Modal Logic for Other-World Agnostics: Neutrality and Halldén Incompleteness

The logic of ‘elsewhere,’ i.e., of a sentence operator interpretable as attaching to a formula to yield a formula true at a point in a Kripke model just in case the first formula is true at all other points in the model, has been applied in settings in which the points in question represent spatial positions (explaining the use of the word ‘elsewhere’), as well as in the case in which they represent moments of time. This logic is applied here to the alethic modal case, in which the points are thought of as possible worlds, with the suggestion that its deployment clarifies aspects of a position explored by John Divers un-der the name ‘modal agnosticism.’ In particular, it makes available a logic whose Halldén incompleteness explicitly registers the agnostic element of the position – its neutrality as between modal realism and modal anti-realism.     

盆腔炎性疾病的预防

盆腔炎性疾病（pelvic inflammatory disease,PID）是影响妇女健康的常见病,针对其发病的诱因,预防PID可以从以下几个方面进行：（1）加强性教育,减少性传播疾病;（2）积极做好妇女的卫生保健指导工作;（3）重视筛查、早期诊断及一次性根治下生殖道感染;（4）提高医务人员的理论水平和技术,避免医源性感染;（5）持续正确选择避孕措施;（6）避免阴道冲洗。此外,长期放置宫内节育器不会增加PID的风险;口服避孕药对PID无明显预防作用,而仅仅与减轻其严重症状有关。     

The Tense Logic for Master Argument in Prior’s Reconstruction

In this paper we examine Prior’s reconstruction of Master Argument [4] in some modal-tense logic. This logic consists of a purely tense part and Diodorean definitions of modal alethic operators. Next we study this tense logic in the pure tense language. It is the logic K _t 4 plus a new axiom (P): ‘p Λ G p ⊃ P G p’. This formula was used by Prior in his original analysis of Master Argument. (P) is usually added as an extra axiom to an axiomatization of the logic of linear time. In that case the set of moments is a total order and must be left-discrete without the least moment. However, the logic of Master Argument does not require linear time. We show what properties of the set of moments are exactly forced by (P) in the reconstruction of Prior. We make also some philosophical remarks on the analyzed reconstruction. Presented by Jacek Malinowski