Every Finitely Reducible Logic has the Finite Model Property with Respect to the Class of ♦-Formulae

In this paper a unified framework for dealing with a broad family of propositional multimodal logics is developed. The key tools for presentation of the logics are the notions of closure relation operation and monotonous relation operation. The two classes of logics: FiRe-logics (finitely reducible logics) and LaFiRe-logics (FiRe-logics with local agreement of accessibility relations) are introduced within the proposed framework. Further classes of logics can be handled indirectly by means of suitable translations. It is shown that the logics from these classes have the finite model property with respect to the class of -formulae, i.e. each -formula has a -model iff it has a finite -model. Roughly speaking, a -formula is logically equivalent to a formula in negative normal form without occurrences of modal operators with necessity force. In the proof we introduce a substantial modification of Claudio Cerrato's filtration technique that has been originally designed for graded modal logics. The main core of the proof consists in building adequate restrictions of models while preserving the semantics of the operators used to build terms indexing the modal operators.     

Predicate Logics on Display

The paper provides a uniform Gentzen-style proof-theoretic framework for various subsystems of classical predicate logic. In particular, predicate logics obtained by adopting van Behthem's modal perspective on first-order logic are considered. The Gentzen systems for these logics augment Belnap's display logic by introduction rules for the existential and the universal quantifier. These rules for x and x are analogous to the display introduction rules for the modal operators and and do not themselves allow the Barcan formula or its converse to be derived. En route from the minimal modal predicate logic to full first-order logic, axiomatic extensions are captured by purely structural sequent rules.     

THE DOCTRINE OF THE TRINITY AS A MODEL FOR STRUCTURING THE RELATIONS BETWEEN SCIENCE AND THEOLOGY

Abstract. A strategy for deeding systematically with such complex relationships as those between science and theology is presented after a brief overview of the historical record and illustrated in terms of the concept of divinity. The application of that strategy to the title relationships yields a multilogical/multilevel solution which presents certain analogies to or isomorphisms with the doctrine of the Trinity. These concern mainly the multilogical/multilevel character of both conceptualizations and the relational and contextual reasoning required to conceive them. Furthermore, certain characteristics of the doctrine facilitate the dialogue between theologians and scientists on account of their similarity with such scientific concepts as diversity in unity, multiplicity of relationships, nonseparability, and nonclassical logic.     

On Alternative Geometries,Arithmetics, and Logics; a Tribute to Łukasiewicz

The paper discusses the similarity between geometry, arithmetic, and logic, specifically with respect to the question of whether applied theories of each may be revised. It argues that they can - even when the revised logic is a paraconsistent one, or the revised arithmetic is an inconsistent one. Indeed, in the case of logic, it argues that logic is not only revisable, but, during its history, it has been revised. The paper also discusses Quine's well known argument against the possibility of logical deviancy.     

Monotonicity in Practical Reasoning

Classic deductive logic entails that once a conclusion is sustained by a valid argument, the argument can never be invalidated, no matter how many new premises are added. This derived property of deductive reasoning is known as monotonicity. Monotonicity is thought to conflict with the defeasibility of reasoning in natural language, where the discovery of new information often leads us to reject conclusions that we once accepted. This perceived failure of monotonic reasoning to observe the defeasibility of natural-language arguments has led some philosophers to abandon deduction itself (!), often in favor of new, non-monotonic systems of inference known as `default logics'. But these radical logics (e.g., Ray Reiter's default logic) introduce their desired defeasibility at the expense of other, equally important intuitions about natural-language reasoning. And, as a matter of fact, if we recognize that monotonicity is a property of the form of a deductive argument and not its content (i.e., the claims in the premise(s) and conclusion), we can see how the common-sense notion of defeasibility can actually be captured by a purely deductive system.     

Argumentation and Evidence

This essay explores the role of informal logicand its application in the context of currentdebates regarding evidence-based medicine. This aim is achieved through a discussion ofthe goals and objectives of evidence-basedmedicine and a review of the criticisms raisedagainst evidence-based medicine. Thecontributions to informal logic by StephenToulmin and Douglas Walton are explicated andtheir relevance for evidence-based medicine isdiscussed in relation to a common clinicalscenario: hypertension management. This essayconcludes with a discussion on the relationshipbetween clinical reasoning, rationality, andevidence. It is argued that informal logic hasthe virtue of bringing explicitness to the roleof evidence in clinical reasoning, and bringssensitivity to understanding the role ofdialogical context in the need for evidence inclinical decision making.     

Intuitionistic Autoepistemic Logic

In this paper we address the problem of combining a logic with nonmonotonic modal logic. In particular we study the intuitionistic case. We start from a formal analysis of the notion of intuitionistic consistency via the sequent calculus. The epistemic operator M is interpreted as the consistency operator of intuitionistic logic by introducing intuitionistic stable sets. On the basis of a bimodal structure we also provide a semantics for intuitionistic stable sets.     

基于非逻辑机制的条件推理模式：P—Q映射模型及其实证检验

研究结合数学分析方法,提出了基于非逻辑机制的条件推理模型：P-Q映射模型。并根据这个模型,对人们在不同命题类型奈件下的推理行为进行了预测。预测结果显示,当推理前提为LH和HL型命题时,基于P-Q映射模型的预测结果与基于条件概率模型的预测结果完全一致。但当推理前提为LL和HH型命题时,两种模型给出的预测结果存在差异。实验结果表明,当前提命题为LL和HH型命题时,被试的条件推理行为与P-Q映射模型的预言完全一致。     

Inexact Knowledge with Introspection

Standard Kripke models are inadequate to model situations of inexact knowledge with introspection, since positive and negative introspection force the relation of epistemic indiscernibility to be transitive and euclidean. Correlatively, Williamson’s margin for error semantics for inexact knowledge invalidates axioms 4 and 5. We present a new semantics for modal logic which is shown to be complete for K45, without constraining the accessibility relation to be transitive or euclidean. The semantics corresponds to a system of modular knowledge, in which iterated modalities and simple modalities are not on a par. We show how the semantics helps to solve Williamson’s luminosity paradox, and argue that it corresponds to an integrated model of perceptual and introspective knowledge that is psychologically more plausible than the one defended by Williamson. We formulate a generalized version of the semantics, called token semantics, in which modalities are iteration-sensitive up to degree n and insensitive beyond n. The multi-agent version of the semantics yields a resource-sensitive logic with implications for the representation of common knowledge in situations of bounded rationality.