In this paper we investigate Boolean connexive logics in a language with modal operators: □, ◊. In such logics, negation, conjunction, and disjunction behave in a classical, Boolean way. Only implication is non-classical. We construct these logics by mixing relating semantics with possible worlds. This way, we obtain connexive counterparts of basic normal modal logics. However, most of their traditional axioms formulated in terms of modalities and implication do not hold anymore without additional constraints, since our implication is weaker than (...) the material one. In the final section, we present a tableau approach to the discussed modal logics. (shrink)

Standard deontic logic (SDL) is defined on the basis of possible world semantics and is a logic of alethic-deontic modalities rather than deontic modalities alone. The interpretation of the concepts of obligation and permission comes down exclusively to the logical value that a sentence adopts for the accessible deontic alternatives. Here, we set forth a different approach, this being a logic which additionally takes into consideration whether sentences stand in relation to the normative system or to the system of values (...) under which we predicate the deontic qualifications. By taking this aspect into account, we arrive at a logical system which preserves laws proper to a deontic logic but where the standard paradoxes of deontic logic do not arise. It is a logic of strictly-deontic modalities DR. (shrink)

Here, we discuss historical, philosophical and technical problems associated with relating logic and relating semantics. To do so, we proceed in three steps. First, Section 1 is devoted to providing an introduction to both relating logic and relating semantics. Second, we address the history of relating semantics and some of the main research directions and their philosophical applications. Third, we discuss some technical problems related to relating semantics, particularly whether the direct incorporation of the relation into the language of relating (...) logic is needed. The starting point for our considerations presented here is the 1st Workshop On Relating Logic and the selected papers for this issue. (shrink)

In the paper, we examine tableau systems for R. Epstein’s logics of content relationship: D (Dependence Logic), DD (Dual Dependence Logic), Eq (Logic of Equality of Content), S (Symmetric Relatedness Logic) and R (Nonsymmetric Relatedness Logic) (cf. Epstein in Philos Stud 36:137–173, 1979, Epstein in Rep. Math. Logic 21:19–34, 1987, Klonowski in Logic Log Philos 30(4):579–629, 2021, Krajewski in J Non Class Logic 8:7–33, 1991). The first tableau systems for those logics were defined by Carnielli. However, his approach has some (...) limitations, for example, it requires a proof of functional completeness and axiomatization. Notwithstanding the first two constraints, it does not include all Epstein logics, e.g., logic Eq. Unlike Carnielli’s approach, here we use set-assignment semantics to determine those logics. Since syntax and semantics of a given logic usually determine a minimal syntax and structure of a tableau system for the logic along with other properties, we propose a uniform tableau framework for the logics determined by set-assignment semantics. What distinguishes our tableau systems is that they combine the features of tableaux for propositional logics and syllogistic logics when the problem of content of propositions is analysed in tableau proofs. To denote the content of propositions in the proofs, we use generalised labels (see Jarmużek and Goré in Landscapes in Logic, College Publications, London, 2021). (shrink)

In the paper a generalised method for obtaining an adequate axiomatic system for any relating logic expressed in the language with Boolean connectives and relating implication, determined by the limited positive relational properties is studied. The method of defining axiomatic systems for logics of a given type is called an algorithm since the analysis allows for any logic determined by the limited positive relational properties to define the adequate axiomatic system automatically, step-by-step. We prove in the paper that the algorithm (...) really works and we show how it can be applied to BLRI. (shrink)

O pewnym językowym rozszerzeniu logiki MR: podejście semantyczne i tabelau W artykule przedstawiamy rozszerzenie minimalnej, normalnej logiki pozycyjnej, czyli logiki z operatorem realizacji. Logika pozycyjna to logika filozoficzna, która umożliwia odniesienie zdań do kontekstów, które można rozumieć na wiele sposobów. Wzbogacamy podstawowy język minimalnej logiki pozycyjnej o dodatkowe wyrażenia zbudowane z predykatów i stałych pozycyjnych. Akceptujemy również wyrażenia zbudowane z operatorem realizacji oraz wiele pozycji, takich jak: Dzięki temu zwiększyliśmy wyrazistość minimalnej logiki pozycyjnej. W artykule wskazujemy na wiele przykładów na (...) to, że dzięki tej niewielkiej zmianie mogą powstać złożone teorie oparte na proponowanym rozszerzeniu. Jako teorię dowodu dla naszej logiki zakładamy metody tableau, pokazujące twierdzenia o poprawności i zupełności. Na koniec jednak pokazujemy, że badana tutaj logika jest tylko rozszerzeniem językowym MR: wszystkie twierdzenia o przedłużeniu mają swoje odpowiedniki w czystych twierdzeniach MR. Jednak teorie oparte na proponowanym rozszerzeniu mogą wyrazić znacznie więcej niż teorie oparte na czystej MR. (shrink)

We define and investigate from a logical point of view a family of consequence relations defined in probabilistic terms. We call them relations of supporting, and write: |≈w where w is a probability function on a Boolean language. A |≈w B iff the fact that A is the case does not decrease a probability of being B the case. Finally, we examine the intersection of |≈w, for all w, and give some formal properties of it.

In the article "Podstawy analizy metodologicznej kanonów Milla" [2] Jerzy Łoś proposed an operator that refered sentences to temporal moments. Let us look, for example, at a sentence ‘It is raining in Toruń’. From a logical point of view it is a propositional function, which does not have any logical value, unless we point at a temporal context from a fixed set of such contexts. If the sentence was considered today as a description of a state of affairs, it could (...) be true. If it was considered yesterday, it could be false. 1 The operator enables us to connect any sentence p with any temporal context t. Such a complex sentence we read as: a sentence p is realized at a temporal context t (a point of time, an interval of some kind, etc). (shrink)

In this paper, we apply relating semantics to the widely discussed problem of free choice between permitted actions or situations in normative systems. Leaving aside contexts in which the free choice principle is obviously unacceptable or uncontroversially valid, we concentrate on free choice for explicit permissions. In order to construct a formal representation of explicit permissions, we introduce a special constant, $\texttt {permit}$, which is analogous to the constant $\texttt {violation}$ used in the Andersonian–Kangerian approach to deontic logic with respect (...) to prohibition and obligation. Consequently, we define a permission operator on the basis of the $\texttt {permit}$ constant and a relation of legitimization. The general idea is that $P \varphi $ is true if and only if $\texttt {permit}$ is true, which means that a permission is actually issued and $\varphi $ is legitimized by $\texttt {permit}$. The intuitive notion of legitimization is formally represented by an operator of relating implication: a non-classical implication that is semantically defined by adding a constraint to the classical meaning of implication to the effect that arguments are related by a special relation. The properties of this relation are based on an informal, intuitive meaning of legitimization and determine the properties of the permission operator. We show that the resulting permission operator possesses the free choice property and avoids certain unwanted consequences that follow from alternative approaches. (shrink)

In the paper we examine the problem of logical systems that are extensions of Classical Propositional Logic with new, intensional connectives of agency: monadic and dyadic _bringing it about that_. These systems are usually studied within the neighbourhood semantics. Here we propose a different strategy. We study all of the accepted laws and rules of logic of agency and define a translation of the agency operators into connectives interpreted in relating semantics. After this translation we can make a reduction to (...) more basic semantic properties that are required by the particular groups of laws and axioms. Finally, we define proper semantic structures and prove that they are complete with respect to all possible logical systems determined by the combinations of the axioms and rules. (shrink)

The article presents a formalization of Anselm's so-called Ontological Arguments from Proslogion . The main idea of our research is to stay to the original text as close as is possible. We show, against some common opinions, that (i) the logic necessary for the formalization must be neither a purely sentential modal calculus, nor just non-modal first-order logic, but a modal first-order theory; (ii) such logic cannot contain logical axiom ⌜ A → ⋄ A ⌝; (iii) none of Anselm's reasonings (...) requires the assumptions that God is a consistent object or that existence of God is possible (in symbols "⋄Eg"); (iv) no such thing as the so-called Anselm's Principle (in symbols "□(Eg → □Eg)") is involved in any of the proofs; (v) Anselm's claims (that God exists in reality and that God necessarily exists in reality) can be obtained independently, hence there is no need for presenting them in an opposite order than Anselm did. Moreover we show a single line of reasoning underlying the whole Proslogion and allowing Anselm to deduce many theorems concerning God's nature. Last but not least we study the possibility of proving the uniqueness of God within the outlined theory. (shrink)

Here, we discuss logical, philosophical and technical problems associated to relating logic and relating semantics. To do so, we proceed in three steps. The first step is devoted to providing an introduction to both relating logic and relating semantics. We discuss this problem on the example of different languages. Second, we address some of the main research directions and their philosophical applications to non-classical logics, particularly to connexive logics. Third, we discuss some technical problems related to relating semantics, and its (...) application to philosophy of science, language and pragmatics. (shrink)

David Makinson, "Bridges from Classical to Nonmonotonic Logic", King’s College Publications, London, 2005, pp. 216, ISBN 1-904987-00-1.

The paper is devoted to an approach to analytic tableaux for propositional logic, but can be successfully extended to other logics. The distinguishing features of the presented approach are:(i) a precise set-theoretical description of tableau method; (ii) a notion of tableau consequence relation is defined without help of a notion of tableau, in our universe of discourse the basic notion is a branch;(iii) we define a tableau as a finite set of some chosen branches which is enough to check; hence, (...) in our approach a tableau is only a way of choosing a minimal set of closed branches;(iv) a choice of tableau can be arbitrary, it means that if one tableau starting with some set of premisses is closed in the defined sense, then every branch in the power set of the set of formulas, that starts with the same set, is closed. (shrink)

Poznawalność jako modalność de re: pewne rozwiązanie paradoksu Fitcha W artykule staramy się znaleźć nowe, intuicyjne rozwiązanie paradoksu Fitcha. Twierdzimy, że tradycyjne wyrażenie zasady poznawalności opiera się na błędnym rozumieniu poznawalności jako modalności de dicto. Zamiast tego proponujemy rozumieć poznawalność jako modalność de re. W artykule przedstawiamy minimalną logikę poznawalności, w której zasada poznawalności jest ważna, ale paradoks Fitcha już nie obowiązuje. Logikę charakteryzujemy semantycznie, a także poprzez podejście aksjomatyczne i tabelaryczne.

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. (shrink)

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 $:p \wedge Gp \supset PGp'$. This formula was used by Prior in his original analysis of Master Argument. 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 in the reconstruction of Prior. We make also some philosophical remarks on the analyzed reconstruction. (shrink)

In this paper, we indicate how Jan Woleński’s non-linguistic concept of the norm allows us to clarify the deontic relationship between sentences and the given normative system. A relationship of this kind constitutes a component of the metalogic of relating deontic logic, which subjects the logical value of the deontic sentence to the logical value of the constituent sentence and its relationship with a given normative system in the accessible possible worlds.

In this paper we present a tableau system for deontic logics with the operator of explicit permission. By means of this system the decidability of the considered logics can be proved. We will sketch how these logics are semantically defined by means of relating semantics and how they provide a simple solution to the free choice permission problem. In short, these logics employ relating implication and a certain propositional constant. These two are in turn used to define deontic operators similarly (...) as in Andersonian-Kangerian reduction, which uses different intensional implications and constants. (shrink)

By a pure modal logic of names we mean a quantifier-free formulation of such a logic which includes not only traditional categorical, but also modal categorical sentences with modalities de re and which is an extension of Propositional Logic. For categorical sentences we use two interpretations: a “natural” one; and Johnson and Thomason’s interpretation, which is suitable for some reconstructions of Aristotelian modal syllogistic :271–284, 1989; Thomason in J Philos Logic 22:111–128, 1993 and J Philos Logic 26:129–141, 1997. In both (...) cases we use Johnson-like models. We also analyze different kinds of versions of PMLN, for both general and singular names. We present complete tableau systems for the different versions of PMLN. These systems enable us to present some decidability methods. It yields “strong decidability” in the following sense: for every inference starting with a finite set of premises we can specify a finite number of steps to check whether it is logically valid. This method gives the upper bound of the cardinality of models needed for the examination of the validity of a given inference. (shrink)

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.

David Lewis’s latest theory of causation defines the causal link in terms of the relation of influence between events. It turns out, however, that one event’s influencing another is neither a necessary nor sufficient condition for its being a cause of that event. In the article one particular case of causality without influence is presented and developed. This case not only serves as a counterexample to Lewis’s influence theory, but also threatens earlier counterfactual analyses of causation by admitting a particularly (...) troublesome type of preemption. The conclusion of the article is that Lewis’s influence method of solving the preemption problem fails, and that we need a new and fresh approach to the cases of redundant causation if we want to hold on to the counterfactual analysis of causation. (shrink)

In the late 2010s, various international committees, expert groups, and national strategy boards have voiced the demand to ‘open’ the algorithmic black box, to audit, expound, and demystify artificial intelligence. The opening of the algorithmic black box, however, cannot be seen only as an engineering challenge. In this article, I argue that only the sort of transparency that arises from critique—a method of theoretical examination that, by revealing pre-existing power structures, aims to challenge them—can help us produce technological systems that (...) are less deceptive and more just. I relate the question of AI transparency to the broader challenge of responsible making, contending that future action must aim to systematically reconcile design—as a way of concealing—with critique—as a manner of revealing. (shrink)

Anthropologists often have fieldwork experiences that are not explicitly analysed in their writings, though they nevertheless contribute to and shape their ethnographic understandings, and can resonate throughout their work for many years. The task of this volume is precisely to uncover these layers of anthropological knowledge-making. Contributors take on the challenge of reconstructing the ways in which they originally entered the worlds of research subjects - their anthropological Others - by focusing on pre-textual and deeply phenomenological processes of perceiving, noting, (...) listening and sensing. Drawing on a wide range of research experiences - with the Dogon in Mali, immigrant football players in Spain, the Inuit of the Far North, Filipino transnational families, miners in Poland and students in Scotland - this book goes beyond an exploration of the development of increased ethnographic sensitivity towards words or actions. It also commences the foundational project of developing a new language for building anthropological works, one stemming from recurring acts of participation, and rooted primarily in the pre-textual worlds of the tacit, often non-visible, and intense experiences that exceed the limitations of conventional textual accounts. (shrink)

Avant-propos -- L'œil énucléé -- L'œil du Dieu caché -- L'œil originel -- L'œil silencieux -- L'œil du non-savoir -- L'œil météorologique -- L'œil maternel -- L'œil incestueux -- L'œil persuasif -- L'œil orgiastique -- L'œil obscurci -- L'œil sociologique -- L'œil testamentaire -- L'œil transversal -- L'œil sacré -- L'œil artaudien -- L'œil du flâneur -- L'œil urbain -- L'œil méditatif -- L'œil éclaboussé -- En guise de vision : l'œil laminé.

This book is a collection of skeptical social essays in which the author reveals that much of our popular beliefs, psychology and science are defective, because, although we live in the 21st century, our approach to them is deeply rooted in our culture, and biased by history and evolution. These essays help the reader take a step sideways, think independently, and not fall victim to fads, fakes, and frauds. Anyone who values a deeper understanding of contemporary social reality and the (...) changes taking place in it should read this book, from students to scientists and intellectuals. Through these essays we learn to look under the veneer of reality, behind the altars of science, under the scenery of pop-psychology and behind the facade of therapeutic culture. Thanks to essays on suicide, euthanasia and more, we also come close to the edge of life and death. Contrary to many meticulous social critical analyzes, in sharing his thoughts the author takes us on a picturesque journey through bounty hunters, ludicrous machines, compulsive hoarding, Charlie Chaplin, and much more. (shrink)

The book _Metaphysics in Contemporary Physics_ offers various perspectives on the relation and mutual influence between modern physical theories and analytic metaphysics.