This volume of the Logica Yearbook series brings together articles presented at the annual international symposium Logica 2010, 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 presented at the annual international symposium Logica 2013, Hejnice, the Czech Republic. The articles range over mathematical and philosophical logic, history and philosophy of logic, and the analysis of natural language.

This paper introduces a generalized version of inquisitive semantics, denoted as GIS, and concentrates especially on the role of disjunction in this general framework. Two alternative semantic conditions for disjunction are compared: the first one corresponds to the so-called tensor operator of dependence logic, and the second one is the standard condition for inquisitive disjunction. It is shown that GIS is intimately related to intuitionistic logic and its Kripke semantics. Using this framework, it is shown that the main results concerning (...) inquisitive semantics, especially the axiomatization of inquisitive logic, can be viewed as particular cases of more general phenomena. In this connection, a class of non-standard superintuitionistic logics is introduced and studied. These logics share many interesting features with inquisitive logic, which is the strongest logic of this class. (shrink)

A conversation can be conceived as aiming to circumscribe a set of possibilities that are relevant to the goals of the conversation. This set of possibilities may be conceived as determined by the goals and objective circumstances of the interlocutors and not by their propositional attitudes. An indicative conditional can be conceived as circumscribing a set of possibilities that have a certain property: If the set of relevant possibilities is subsequently restricted to one in which the antecedent holds, then it (...) will be restricted as well to one in which the consequent holds. We will identify a number of desiderata concerning the validity of arguments; we will develop a formally precise semantics for conditionals conceived in this way that satisfies the desiderata, and we will present a deductive calculus that is sound and complete with respect to the semantics. Finally, we will argue that the semantics compares well, both formally and foundationally, with two other semantic theories of indicative conditionals that satisfy the desiderata, namely, those of Gillies and Bledin. (shrink)

This paper introduces the inquisitive extension of R, denoted as InqR, which is a relevant logic of questions based on the logic R as the background logic of declaratives. A semantics for InqR is developed, and it is shown that this semantics is, in a precisely defined sense, dual to Routley-Meyer semantics for R. Moreover, InqR is axiomatized and completeness of the axiomatic system is established. The philosophical interpretation of the duality between Routley-Meyer semantics and the semantics for InqR is (...) also discussed. (shrink)

This paper introduces and explores a conservative extension of inquisitive logic. In particular, weak negation is added to the standard propositional language of inquisitive semantics, and it is shown that, although we lose some general semantic properties of the original framework, such an enrichment enables us to model some previously inexpressible speech acts such as weak denial and ‘might’-assertions. As a result, a new modal logic emerges. For this logic, a Fitch-style system of natural deduction is formulated. The main result (...) of this paper is a theorem establishing the completeness of the system with respect to inquisitive semantics with weak negation. At the conclusion of the paper, the possibility of extending the framework to the level of first order logic is briefly discussed. (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.

In this paper we introduce a class of inquisitive Heyting algebras as algebraic structures that are isomorphic to algebras of finite antichains of bounded implicative meet semilattices. It is argued that these structures are suitable for algebraic semantics of inquisitive superintuitionistic logics, i.e. logics of questions based on intuitionistic logic and its extensions. We explain how questions are represented in these structures and provide several alternative characterizations of these algebras. For instance, it is shown that a Heyting algebra is inquisitive (...) if and only if its prime filters and filters generated by sets of prime elements coincide and prime elements are closed under relative pseudocomplement. We prove that the weakest inquisitive superintuitionistic logic is sound with respect to a Heyting algebra iff the algebra is what we call a homomorphic p-image of some inquisitive Heyting algebra. It is also shown that a logic is inquisitive iff its Lindenbaum–Tarski algebra is an inquisitive Heyting algebra. (shrink)

We investigate an information based generalization of the incompatibility-frame treatment of logics with non-classical negation connectives. Our framework can be viewed as an alternative to the neighbourhood semantics for extensions of lattice logic by various negation connectives, investigated by Hartonas. We set out the basic semantic framework, along with some correspondence results for extensions. We describe three kinds of constructions of canonical models and show that double negation law is not canonical with respect to any of these constructions. We also (...) compare our semantics to Hartonas’. (shrink)

In this paper, Carnap's modal logic C is reconstructed. It is shown that the Carnapian approach enables us to create some epistemic logics in a relatively straightforward way. These epistemic modifications of C are axiomatized and one of them is compared with intuitionistic logic. At the end of the paper, some connections between this epistemic logic and Medvedev's logic of finite problems and inquisitive semantics are shortly discussed.

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)

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.

This volume of the Logica Yearbook series brings together articles presented at the annual international symposium Logica 2012, Hejnice, the Czech Republic. The articles range over mathematical and philosophical logic, history and philosophy of logic, and the analysis of natural language.

This paper explores the relation between the philosophical idea that logic is a science studying logical forms, and a mathematical feature of logical systems called the principle of uniform substitution, which is often regarded as a technical counterpart of the philosophical idea. We argue that at least in one interesting sense the principle of uniform substitution does not capture adequately the requirement that logic is a matter of form and that logical truths are formal truths. We show that some specific (...) logical expressions can produce propositions of different kinds and the resulting diversity of informational types can lead to a justified failure of uniform substitution without undermining the view that logic is a purely formal discipline. (shrink)

The paper extends a framework of information-based semantics for intuitionistic logic with a paraconsistent negation and consistency-sensitive epistemic modalities. In this framework information states represent information collected from various sources and as such they can be inconsistent because they receive contradictory information either from a single inconsistent source or from various mutually incompatible sources. The modalities reflect only those sources that are consistent and trusted. For the paraconsistent logic generated by this framework, we present a Hilbert style system, we prove (...) completeness, the disjunction property, the finite model property and various other results. (shrink)

V tomto článku předkládám některé důvody proti Dvořákovu nedeterministickému pojetí svobodné vůle, které vyložil ve své nedávno publikované knize Kauzalita činitele. Zejména se zabývám Dvořákovým řešením problému náhody, podle kterého je akt svobodné vůle náhodný do té míry, do jaké se nepodřizuje deterministickým zákonům, a do této míry také nemůže být předmětem morálního hodnocení. Proti Dvořákově koncepci stavím vlastní pojetí svobodné vůle, které je variací na to, co Dvořák označuje jako „standardní teorie“. Z hlediska tohoto pojetí je svobodná vůle možná (...) i v deterministickém světě. Analyzuji, v čem spočívá volba mezi alternativními možnostmi, a argumentuji, že je možné mít kontrolu nad vlastním jednáním, i když nemáme kontrolu nad minulostí, která toto jednání jednoznačně determinuje. Zároveň vysvětluji, proč se v ostrém rozporu s Dvořákovou koncepcí domnívám, že člověk v deterministickém světě může nést odpovědnost za své činy. (shrink)

From the perspective of philosophy of science and technologies, we firstly attend to the issue of the role of nanotechnologies within the evolution of technologies. We recognize their utmost importance in the respect that they are technologies of life itself. We further explain that the nano-level is the domain of intersection of the rules of quantum physics and traditional Newtonian physics. This is our starting point from which we discuss the issue of conditions under which minimizing things also changes their (...) functional essence. We use the example of the Drexler vs. Smalley debate to demonstrate the paradigmatic incomparability of the two perspectives and the physical-chemical and engineering-related limits of nanotechnologies. We discuss to what extent are the dangers and ethical implications emerging from Drexler’s contemplations real, be it what he calls the “grey goo” problem or the issues of molecular production. We regard certain problems linked to synthetic biology as more serious. We conclude our text with the consideration that the human civilization should think of the possibilities of nanotechnologies in the development of life as an existential challenge. (shrink)

In this paper, we present Carnap’s modal logic C, which is one of the first attempts to use the concept of possible world in shaping the semantics for modalities. Some older technical results, which concern the logic C, are summarized, namely two different kinds of axiomatization of C, one unusual characterization of C as the only set of formulae having one special property, and semantical and syntactical relations of C to S5. The fact that C is not closed under the (...) universal substitution is shortly discussed. Finally, the predicate version of C, which is not axiomatizable, is defined. (shrink)

In this paper, the notion of structural completeness is explored in the context of a generalized class of superintuitionistic logics involving also systems that are not closed under uniform substitution. We just require that each logic must be closed under D-substitutions assigning to atomic formulas only ∨\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\vee $$\end{document}-free formulas. For these systems we introduce four different notions of structural completeness and study how they are related. We focus on superintuitionistic inquisitive logics (...) that validate a schema called Split and have the disjunction property. In these logics disjunction can be interpreted in the sense of inquisitive semantics as a question forming operator. It is shown that a logic is structurally complete with respect to D-substitutions if and only if it includes the weakest superintuitionistic inquisitive logic. Various consequences of this result are explored. For example, it is shown that every superintuitionistic inquisitive logic can be characterized by a Kripke model built up from D-substitutions. Additionally, we resolve a conjecture concerning superintuitionistic inquisitive logics due to Miglioli et al.. (shrink)

The aim of this paper is to introduce erotetic search scenarios known from Inferential Erotetic Logic by using the framework of epistemic erotetic logic. The key notions used in this system are those of askability and epistemic erotetic implication. Scenarios are supposed to represent all rational strategies of an agent solving the problem posed by the initial question where the interaction with an external information source is seen as a series of updates of the agent’s knowledge.

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.

We give a few results concerning the notions of causal completability and causal closedness of classical probability spaces . We prove that any classical probability space has a causally closed extension; any finite classical probability space with positive rational probabilities on the atoms of the event algebra can be extended to a causally up-to-three-closed finite space; and any classical probability space can be extended to a space in which all correlations between events that are logically independent modulo measure zero event (...) have a countably infinite common-cause system. Collectively, these results show that it is surprisingly easy to find Reichenbach-style ‘explanations' for correlations, underlining doubts as to whether this approach can yield a philosophically relevant account of causality. 1 Introduction2 Basic Definitions and Results in the Literature3 Causal Completability the Easy Way: ‘Splitting the Atom’4 Causal Completability of Classical Probability Spaces: The General Case5 Infinite Statistical Common-Cause Systems for Arbitrary Pairs6 ConclusionAppendix A. (shrink)

A key question has been underexplored in the literature on conscientious objection: if a physician is required to perform ‘medical activities,’ what is a medical activity? This paper explores the question by employing a teleological evaluation of medicine and examining the analogy of military conscripts, commonly cited in the conscientious objection debate. It argues that physicians (and other healthcare professionals) can only be expected to perform and support medical acts – acts directed towards their patients’ health. That is, physicians cannot (...) be forced to provide or support services that are not medical in nature, even if such activities support other socially desirable pursuits. This does not necessarily mean that medical professionals cannot or should not provide non-medical services, but only that they are under no obligation to provide them. (shrink)

Reism or concretism are the labels for a position in ontology and semantics that is represented by various philosophers. As Kazimierz Ajdukiewicz and Jan Woleński have shown, there are two dimensions with which the abstract expression of reism can be made concrete: The ontological dimension of reism says that only things exist; the semantic dimension of reism says that all concepts must be reduced to concrete terms in order to be meaningful. In this paper we argue for the following two (...) theses: (1) Arthur Schopenhauer has advocated a reistic philosophy of language which says that all concepts must ultimately be based on concrete intuition in order to be meaningful. (2) In his semantics, Schopenhauer developed a theory of logic diagrams that can be interpreted by modern means in order to concretize the abstract position of reism. Thus we are not only enhancing Jan Woleński’s list of well-known reists, but we are also adding a diagrammatic dimension to concretism, represented by Schopenhauer. (shrink)

In this chapter we take stock of some of the complexities of the sprawling field of AI ethics. We consider questions like "what is the proper scope of AI ethics?" And "who counts as an AI ethicist?" At the same time, we flag several potential uses and abuses of AI ethics. These include challenges for the AI ethicist, including what qualifications they should have; the proper place and extent of futuring and speculation in the field; and the dilemmas concerning how (...) we use our public and academic resources. (shrink)

In this chapter we identify three potentially morally problematic behaviours that are common among users of dating and hook-up apps (DHAs) and provide arguments as to why they may or may not be considered (a) in a category of their own, distinct from similar behaviours outside of DHAs; (b) caused or facilitated by affordances and business logic of DHAs; (c) as indeed morally wrong. We also consider ways in which morally problematic behaviours can be anticipated, mitigated, or even prevented by (...) analysis of the ethical and moral dimensions of technologies and their afforded uses. Finally, we offer some possible directions for future work on these topics in particular and on the ethical consequences of DHAs in general. (shrink)

Mental arithmetic is characterised by a tendency to overestimate addition and to underestimate subtraction results: the operational momentum effect. Here, motivated by contentious explanations of this effect, we developed and tested an arithmetic heuristics and biases model that predicts reverse OM due to cognitive anchoring effects. Participants produced bi-directional lines with lengths corresponding to the results of arithmetic problems. In two experiments, we found regular OM with zero problems but reverse OM with non-zero problems. In a third experiment, we tested (...) the prediction of our model. Our results suggest the presence of at least three competing biases in mental arithmetic: a more-or-less heuristic, a sign-space association and an anchoring bias. We conclude that mental arithmetic exhibits shortcuts for decision-making similar to traditional domains of reasoning and problem-solving. (shrink)

In mid-2019, the controversy regarding South African runner Caster Semenya’s eligibility to participate in competitions against other female runners culminated in a Court of Arbitration for Sport judgement. Semenya possessed high endogenous testosterone levels (arguably a performance advantage), secondary to a disorder of sexual development. In this commentary, Aristotelean teleology is used to defend the existence of ‘male’ and ‘female’ as discrete categories. It is argued that once the athlete’s sex is established, they should be allowed to compete in the (...) category of their sex without obligatory medical treatment. Indeed, other athletes who possess advantageous genetic or phenotypic traits that fall outside of the human norm have been allowed to compete as humans without restraint. In both cases, if an athlete possesses the essential attributes of being a human or being male or female they should be permitted to compete in those respective categories; athletes’ eligibilities should not be based upon accidental attributes. (shrink)

Disorders of sexual differentiation lead to what is often referred to as an intersex state. This state has medical, as well as some legal, recognition. Nevertheless, the question remains whether intersex persons occupy a state in between maleness and femaleness or whether they are truly men or women. To answer this question, another important conundrum needs to be first solved: what defines sex? The answer seems rather simple to most people, yet when morphology does not coincide with haplotypes, and genetics (...) might not correlate with physiology the issue becomes more complex. This paper tackles both issues by establishing where the essence of sex is located and by superimposing that framework onto the issue of the intersex. This is achieved through giving due consideration to the biology of sexual development, as well as through the use of a teleological framework of the meaning of sex. Using a range of examples, the paper establishes that sex cannot be pinpointed to one biological variable but is rather d... (shrink)

Wischik presents an extensive reply to our paper on conscientious objection, which explores the implications of distinguishing ‘medical acts’ from ‘socioclinical acts’. He provides an extensive leg...

Kunstmatige intelligentie (AI) en systemen die met machine learning (ML) werken, kunnen veel onderdelen van het medische besluitvormingsproces ondersteunen of vervangen. Ook zouden ze artsen kunnen helpen bij het omgaan met klinische, morele dilemma’s. AI/ML-beslissingen kunnen zo in de plaats komen van professionele beslissingen. We betogen dat dit belangrijke gevolgen heeft voor de relatie tussen een patiënt en de medische professie als instelling, en dat dit onvermijdelijk zal leiden tot uitholling van het institutionele vertrouwen in de geneeskunde.