Combining relevant and classical modal logic is an approach to overcoming the logical omniscience problem and related issues that goes back at least to Levesque’s well known work in the 1980s. The present authors have recently introduced a variant of Levesque’s framework where explicit beliefs concerning conditional propositions can be formalized. However, our framework did not offer a formalization of implicit belief in addition to explicit belief. In this paper we provide such a formalization. Our main technical result is a (...) modular completeness theorem. (shrink)

We introduce a general representation of unary hyperintensional modalities and study various hyperintensional modal logics based on the representation. It is shown that the major approaches to hyperintensionality known from the literature, that is state-based, syntactic and structuralist approaches, all correspond to special cases of the general framework. Completeness results pertaining to our hyperintensional modal logics are established.

The article introduces substructural epistemic logics of belief supported by evidence. The logics combine normal modal epistemic logics with distributive substructural logics. Pieces of evidence are represented by points in substructural models and availability of evidence is modelled by a function on the point set. The main technical result is a general completeness theorem. Axiomatisations are provided by means of two-sorted Hilbert-style calculi. It is also shown that the framework presents a natural solution to the problem of logical omniscience.

We provide a complete binary implicational axiomatization of the positive fragment of propositional dynamic logic. The intended application of this result are completeness proofs for non-classical extensions of positive PDL. Two examples are discussed in this article, namely, a paraconsistent extension with modal De Morgan negation and a substructural extension with the residuated operators of the non-associative Lambek calculus. Informal interpretations of these two extensions are outlined.

The paper introduces a new kind of models for the logic of proofs LP, the group justification models. While being an elaboration of Fitting models, the group justification models are a special case of the models of general awareness. Soundness and completeness results of LP with respect to the new semantics are established. The paper also offers an interpretation of the group models, which pertains to awareness and group epistemic dynamics.

This article opposes a view widely accepted in studies concerning the history of modal logic, according to which (i) the approach of C. I. Lewis towards constructing modern modal logic was purely syntactical (i.e. limited to the construction of axiomatic systems S1-S5 of propositional modal logic), and (ii) the notion of a possible world was incorporated into modern logic and philosophy mainly by authors such as Rudolf Carnap and Saul Kripke. The article presents Lewis' definition of a possible world, and (...) his formulation of the truth-conditions of statements containing strict implication as their main connective in terms of possible worlds. The main question of the article is whether it is possible to consider Lewis' work in this area as an early stage of the development of possible world semantics, and if so, in what sense? The article concludes by answering affirmatively, due to soundness and completeness proofs with respect to S5 using Lewis' semantics. (shrink)

Fine (J Philos Log 43:549–577, 2014) developed a truthmaker semantics for intuitionistic logic, which is also called exact semantics, since it is based on a relation of exact verification between states and formulas. A natural question arises as to what are the limits of Fine’s approach and whether an exact semantics of similar kind can be constructed for other important non-classical logics. In our paper, we will generalize Fine’s approach and develop an exact semantics for some substructural logics. In particular, (...) we will provide a truthmaker semantics for the Non-associative Lambek calculus and some of its extensions. This generalization will reveal some interesting connections between Fine’s recent work on truthmaker semantics and his early work on relevant logic. (shrink)

The paper relates evidence and justification logics, both philosophically and technically. On the philosophical side, it is suggested that the difference between the approaches to evidence in the two families of logics can be explained as a result of their focusing on two different notions of support provided by evidence. On the technical side, a justification logic with operators pertaining to both kinds of support is shown to be sound and complete with respect to a special class of awareness models. (...) In addition, a realization theorem with respect to K is shown to hold for the logic. (shrink)

The article introduces extended models for the propositional dynamic logic PDL. In extended models, valuation assigns to every state a set of atomic formulas and a PDL program. The program is informally construed as an action preferred by a contextually fixed agent. PDL is then extended by introducing a conditional connective expressing partial correctness claims. The main contribution of the article is the observation that the partial correctness conditional is in fact a substructural implication. It is shown that a variant (...) of the minimal distributive substructural logic DB is a fragment of PDLS, an extension of PDL that contains the partial correctness conditional and fusion. It is also shown that the main results can be extended to a specific class of positive substructural logics. (shrink)

The paper provides an alternative interpretation of ‘pair points’, discussed in Beall et al., "On the ternary relation and conditionality", J. of Philosophical Logic 41(3), 595-612. Pair points are seen as points viewed from two different ‘perspectives’ and the latter are explicated in terms of two independent valuations. The interpretation is developed into a semantics using pairs of Kripke models (‘pair models’). It is demonstrated that, if certain conditions are fulfilled, pair models are validity-preserving copies of positive substructural models. This (...) yields a general soundness and completeness result for a variety of (positive) substructural logics with respect to multimodal Kripke frames with binary accessibility relations. In addition, an epistemic interpretation of pair models is provided. (shrink)

The paper outlines an epistemic logic based on the proof theory of substructural logics. The logic is a formal model of belief that i) is based on true assumptions (BTA belief) and ii) does not suffer from the usual omniscience properties.

The paper outlines a generalisation of the awareness-based epistemic semantics by Fagin and Halpern. Awareness is construed as a relation between agents and pieces of information instead of formulas. The main motive for introducing the generalisation is that it shows substructural logics to be a natural component of information-based epistemic logic: substructural logics can be seen as describing the logical behaviour of pieces of information. Substructural epistemic logics are introduced and some of their properties are discussed. In addition, extensions of (...) substructural epistemic logics invoking group-epistemic and dynamic modalities are sketched. (shrink)

We, the authors, would like to thank Guillaume Aucher for informing us of his “Displaying Updates in Logic”, published in the Journal of Logic and Computation, 26:1865-1912.

The primary aim of the paper is to introduce a new notion of relevance of the antecedent of a true implication statement to its consequent, and to sketch a formalization of the new notion. The formalization is set up in the framework of the so called Logic of Strict Processes , as articulated by the author in collaboration with J. Podroužek. Their approach to the relevance is presented as a natural part of a wider specter of logics, including modal and (...) relevance logics. The formalization is compared with consequence relations in normal modal logic and in the relevance logic R. In conclusion the author outlines the most important problems of LSP, which still remain open. (shrink)

The question, whether there is a sharp difference between an analytic and a synthetic proposition, is one of the famous philosophical topics of the 20th century. The question, however, urges one to ask following questions: "What is an analytic proposition?", or „What is a synthetic proposition?“. The aim of the paper is to contribute to the discussions of the analyticity in that it tries to answer the first of the two. However, the author does not offer his own conception of (...) analyticity. He rather offers a more detailed view on the definitions and characteristics of an analytic proposition in Kant and Frege. (shrink)

We study an expansion of the Distributive Non-associative Lambek Calculus with conjugates of the Lambek product operator and residuals of those conjugates. The resulting logic is well-motivated, under-investigated and difficult to tackle. We prove completeness for some of its fragments and establish that it is decidable. Completeness of the logic is an open problem; some difficulties with applying the usual proof method are discussed.

We outline a novel solution to Moore’s paradox within the framework of update semantics, which explains Moorean absurdity in terms of non-cohesiveness. It is argued that, unlike the outlined solution, Gillies’ treatment of the paradox within this framework is not satisfactory.

The paper sketches an analysis of the notion of a self-fulfilling belief in terms of doxastic modal logic. We point out a connection between self-fulfilling beliefs and Moore’s paradox. Then we look at self-fulfilling beliefs in the context of neighborhood semantics. We argue that the analysis of several interesting self-fulfilling beliefs has to make essential use of propositional quantification.

One way to model epistemic states of agents more realistically is to represent these states by sets of situations rather than possible worlds. In this paper we discuss representations of epistemic update in terms of situations. After linking epistemic update based on deleting epistemic accessibility arrows with update of situations, we discuss two specific kinds of public epistemic update; monotonic update in intuitionistic dynamic epistemic logic, and non-monotonic update in substructural dynamic epistemic logic. Our investigation is mainly conceptual, but leads (...) to completeness results using reduction axioms, and lays the groundwork for future investigation into the concept of situated epistemic update. (shrink)

This volume of the Logica Yearbook series brings together articles presented at the annual international symposium Logica 2018, Hejnice, the Czech Republic. The articles range over mathematical and philosophical logic, history and philosophy of logic, and the analysis of natural language.

This volume of the Logica Yearbook series brings together articles based on selected abstracts accepted for presentation at the annual international symposium Logica 2021, in Hejnice, the Czech Republic. The articles range over mathematical and philosophical logic, history and philosophy of logic, and the analysis of natural language.

Pavel Cmorej has argued that the existence of unverifiable and unfalsifiable empirical propositions follows from certain plausible assumptions concerning the notions of possibility and verification. Cmorej proves, it the context of a bi-modal alethic-epistemic axiom system AM4, that (1) p and it is not verified that p is unverifiable; (2) p or it is falsified that p is unfalsifiable; (3) every unverifiable p is logically equivalent to p and it is not verifiable that p; (4) every unverifiable p entails that (...) p is unverifiable. This article elaborates on Cmorej’s results in three ways. Firstly, we formulate a version of neighbourhood semantics for AM4 and prove completeness. This allows us to replace Cmorej’s axiomatic derivations with simple model-theoretic arguments. Secondly, we link Cmorej’s results to two well-known paradoxes, namely Moore’s Paradox and the Knowability Paradox. Thirdly, we generalise Cmorej’s results, show them to be independent of each other and argue that results (3) and (4) are independent of any assumptions concerning the notion of verification. (shrink)

The paper sketches an analysis of the notion of a self-fulfilling belief in terms of doxastic modal logic. We point out a connection between self-fulfilling beliefs and Moore’s paradox. Then we look at self-fulfilling beliefs in the context of neighborhood semantics. We argue that the analysis of several interesting self-fulfilling beliefs has to make essential use of propositional quantification.

In this work, we illustrate applications of a semantic framework for non-congruential modal logic based on hyperintensional models. We start by discussing some philosophical ideas behind the approach; in particular, the difference between the set of possible worlds in which a formula is true (its intension) and the semantic content of a formula (its hyperintension), which is captured in a rigorous way in hyperintensional models. Next, we rigorously specify the approach and provide a fundamental completeness theorem. Moreover, we analyse examples (...) of non-congruential systems that can be semantically characterized within this framework in an elegant and modular way. Finally, we compare the proposed framework with some alternatives available in the literature. In the light of the results obtained, we argue that hyperintensional models constitute a basic, general and unifying semantic framework for (non-congruential) modal logic. (shrink)

This paper combines propositional dynamic logic ) with propositional inquisitive logic ). The result of this combination is a logical system \ that conservatively extends both \ and \, and, moreover, allows for an interaction of the question-forming operator from \ with the structured modalities from \. We study this system from a semantic as well as a syntactic point of view. These two perspectives are linked via a completeness proof, which also shows that \ is decidable.

This volume of the Logica Yearbook series brings together articles presented at the annual international symposium Logica 2019, Hejnice, the Czech Republic. The articles range over mathematical and philosophical logic, history and philosophy of logic, and the analysis of natural language.

This volume of the Logica Yearbook series brings together articles based on selected abstracts accepted for presentation at the annual international symposium Logica 2020, Hejnice, the Czech Republic, which was cancelled due to the Covid-19 pandemic. The articles range over mathematical and philosophical logic, history and philosophy of logic, and the analysis of natural language.

In this paper we discuss whether the relation between formulas in the relating model can be directly introduced into the language of relating logic, and present some stances on that problem. Other questions in the vicinity, such as what kind of functor would be the incorporated relation, or whether the direct incorporation of the relation into the language of relating logic is really needed, will also be addressed.

In the light of the contribution of Majer, Punčochář and Sedlár, I develop a path-theoretic semantics for the conditional and briefly consider some of its applications.

A defense of the rationality of adductive inference from the criticisms of Bayesian theorists.

This paper studies the learnability of natural concepts in the context of the conceptual spaces framework. Previous work proposed that natural concepts are represented by the cells of optimally partitioned similarity spaces, where optimality was defined in terms of a number of constraints. Among these is the constraint that optimally partitioned similarity spaces result in easily learnable concepts. While there is evidence that systems of concepts generally regarded as natural satisfy a number of the proposed optimality constraints, the connection between (...) naturalness and learnability has been less well studied. To fill this gap, we conduct a computational study employing two standard models of concept learning. Applying these models to the learning of color concepts, we examine whether natural color concepts are more readily learned than nonnatural ones. Our findings warrant a positive answer to this question for both models employed, thus lending empirical support to the notion that learnability is a distinctive characteristic of natural concepts. (shrink)

Conditionals have been studied by philosophers for over two thousand years. This should not be surprising, given how central conditionals are to human reasoning and decision making. This chapter argues that making progress in answering the questions about conditionals which have occupied so many philosophers, past and present, may require the use of methods that go beyond those traditionally used in analytic philosophy. The reasons some might have for believing that experimental methods have no place in, or are redundant for, (...) the philosophical study of conditionals will be found wanting. The chapter provides positive reasons for holding that philosophers studying conditionals may greatly benefit from the use of such methods. These reasons will emerge from a discussion of relatively recent results concerning conditionals, most of which have been obtained by experimentally working psychologists as well as by teams consisting of both such psychologists and philosophers. (shrink)

Though the average person may take patriotism for granted as a natural feeling of loyalty to one's country, among philosophers the nature, moral standing, and political significance of patriotism have always been contentious. On the one hand, there are those who defend patriotic loyalty as either a duty or a virtue and extol it as an indispensable condition of a viable polity. On the other hand, critics of patriotism maintain that it is morally suspect to prefer one's country and compatriots, (...) and doing so offends against impartial justice and hinders universal human solidarity. Today patriotism is a topic of debate not only in moral philosophy but also in political theory, where it is often brought up as a test case in the confrontation between liberals and communitarians. These debates have produced much high-quality writing, the best of which is here presented in this wide-ranging collection of essays by philosophers and political theorists. All the main varieties of patriotism are covered—moderate and extreme, as well as ethnic/cultural and political—and both critics and defenders are given a hearing. Editor Igor Primoratz has also included articles that discuss the history of the term in moral and political discourse in the English-speaking world, the distinctively American type of patriotism, the relation of patriotism to nationalism and racism, and the tension between patriotism and universal human solidarity, especially as this issue relates to foreign aid. As the first anthology to treat patriotism in its own right, this work emphasizes that patriotism is a distinct moral and political outlook, and is not merely a variety of nationalism or the emotional underpinning of nationalist theories. As such, it will be an important resource for courses in philosophy and political science, and will also serve as an accessible general reader for the interested layperson. (shrink)

A paper on how to adapt your probabilisitc beliefs when learning a conditional.

The liberal view that valid consent is sufficient for a sex act to be morally legitimate is challenged by three major philosophies of sex: the Catholic view of sex as ordained for procreation and properly confined to marriage, the romantic view of sex as bound up with love, and the radical feminist analysis of sex in our society as part and parcel of the domination of women by men. I take a critical look at all three, focusing on Mary Geach''s (...) recent statement of the procreation view, Roger Scruton''s theory of sexual desire as naturally evolving into intimacy and love, and several radical feminist discussions of sex in sexist society which argue that the notion of consent is unhelpful and, indeed, irrelevant. I argue that none of these lines of argument is convincing, and that consent remains the touchstone of morally permissible sex – although, dmittedly, it may not be very helpful in discussing ideals of human sexuality. (shrink)

This paper highlights some connections between work on truth approximation and work in social epistemology, in particular work on peer disagreement. In some of the literature on truth approximation, questions have been addressed concerning the efficiency of research strategies for approximating the truth. So far, social aspects of research strategies have not received any attention in this context. Recent findings in the field of opinion dynamics suggest that this is a mistake. How scientists exchange and take into account information about (...) each others’ beliefs may greatly influence the accuracy and speed with which the scientific community as a whole approximates the truth. On the other hand, social epistemologists concerned with peer disagreement have so far neglected the question of how practices of responding to disagreements with peers fare with respect to the goal of approximating the truth. Again, work on opinion dynamics shows that this may be a mistake, and that how we ought to respond to disagreements with our peers may depend on the specific purposes of our investigations. (shrink)

У монографії поглиблено науково-методологічні підходи та запропоновано практичні рекомендації щодо побудови ефективної системи взаємопов’язаних і цілеспрямованих інноваційних змін в управлінні бізнесом з метою забезпечення його досконалості в умовах інформаційно-комунікаційної технологізації. Розкрито теоретичні засади управлінської інноватики в бізнесі, поглиблено вивчення інформаційно-комунікаційного контексту забезпечення досконалості бізнесу, удосконалено методологію дослідження проблем бізнесу та оцінки рівня його досконалості в умовах інформаційно-комунікаційної технологізації. Досліджено проблеми бізнесу промислових підприємств України та здійснено оцінку рівня досконалості його ведення в умовах інформаційно-комунікаційної технологізації. Запропоновано комплекс управлінських інновацій із забезпечення (...) досконалості бізнесу промислових підприємств України. Видання розраховане на наукових працівників, викладачів ЗВО і коледжів, керівників бізнес-структур, а також усіх, хто має намір поглибити знання з управління бізнесом. (shrink)

Персонализм - это изумительная трагикомическая игра одного актера, разговор человека с самим собой, когда думаешь, что все люди: и плохие, и хорошие, такие, как ты сам, и что мир - человечный. Персоналист - это мудрый человек, чувствующий, что в нем живут тысячи других людей.

Interest in the topic of wisdom-focused education has so far not resulted in empirically validated programs for teaching wisdom. To start filling this void, we explore the emerging empirical evidence concerning the fundamental elements required for understanding how one can foster wisdom, with a particular focus on wise reasoning. We define wise reasoning through a combination of intellectual humility, recognition of world in flux/change, open-mindedness to diverse viewpoints, and search for compromise/integration of diverse perspectives. In this article, we review evidence (...) concerning how wise reasoning can be facilitated through experiences, teaching materials, environments and cognitive strategies. We also focus on educators, reviewing emerging evidence on how the process of explaining and guiding others impacts one’s wisdom. We conclude by discussing the development of wisdom-focused education, proposing that greater attention to the situational demands and the variability in wisdom-related characteristics across social contexts should play a critical role in its development. (shrink)

The article analyzes the effectiveness of quantum theories of mental experience in relation to two ontological problems - the problem of the existence of consciousness in the material world and the problem of the interaction of consciousness and body. A critical analysis of the quantum theories of consciousness by Penrose-Hameroff, M. Tegmark, G. Stapp, M. Fischer and M.B. Mensky shows that they fail to fully explain how complex physical systems generate mental experience without violating the principle of causal closure of (...) the physical world and the principle of epistemological completeness of physics. Quantum mechanics provides specific processes that are the physical basis of the psyche, but do not explain the phenomenal aspect of subjective reality. Nevertheless, the Heisenberg uncertainty principle gives an understanding of how the interaction of consciousness and body within the scientific picture of the world can be carried out without violating the law of energy conservation. It is shown that the quantum theories of consciousness currently being developed have a predominantly panprotopsychic character, which faces a problem due to the fact that the protomental property of physical systems must be expressed quantitatively and correspond to the value included in the physical equations. As a result, it is concluded that in order to develop quantum theories of consciousness more effectively, it is necessary to give an emergent character, not jumping from the quantum level to the psychic, but explaining the mechanism of the emergence of systemic properties during the sequential transition between different ontological regions of existence, including physical, chemical, biological, neurophysiological and psychic. (shrink)