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.

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)

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)

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.

The International Workshop on Combinatorial Algorithms was established in 1989 as the Australasian Workshop on Combinatorial Algorithms. As a consequence of the workshop's success in attracting mathematicians and computer scientists from around the world, it was decided at the 2006 meeting to go global, to change the workshop's name, and to hold it in appropriate venues around the world. The workshop supports basic research on the interface between mathematics and computing, specifically * Algorithms & Data Structures * Complexity Theory * (...) Algorithms on Graphs & Strings * Combinatorial Optimization * Cryptography & Information Security * Computational Biology * Communications Networks and many other related areas. This is Volume 1 in the series of IWOCA proceedings. See http: //www.iwoca.org/. (shrink)

We propose that human self-domestication favored the emergence of a less aggressive phenotype in our species, more precisely phenotype prone to replace (reactive) physical aggression with verbal aggression. In turn, the (gradual) transition to verbal aggression and to more sophisticated forms of verbal behavior favored self-domestication, with the two processes engaged in a reinforcing feedback loop, considering that verbal behavior entails not only less violence and better survival, but also more opportunities to interact longer and socialize with more conspecifics, ultimately (...) enabling the emergence of more complex forms of language. Whereas in the case of self-domestication sexual selection has been proposed to work against physical aggression traits, in the case of verbal insult the selection has been proposed to work in favor of verbal aggression. The tension between these two seemingly opposing forces gets resolved/alleviated by a tendency to replace physical aggression with verbal aggression, and with verbal behavior more generally. This also helps solve the paradox of the Self Domestication Hypothesis regarding aggression, more precisely why aggression in humans has been reduced only when it comes to reactive aggression, but not when it comes to proactive aggression, the latter exhibiting an increase with the advent of modern language. We postulate that this feedback loop was particularly important during the time period before 50 kya, arguably between 200 kya and 50 kya, when humans were not fully modern, neither in terms of their skull/brain morphology and their behavior/culture, nor in terms of their self-domestication. The novelty of our approach lies (i) in giving an active role to early forms of language in interacting with self-domestication processes; (ii) in providing specific linguistic details and functions of this early stage of grammar (including insult and humor); (iii) in supplying neurobiological, ontogenetic, and clinical evidence of a link between (reactive) aggression and (reactive) verbal behavior; (iv) in identifying a variety of proxies of the earlier stages in evolution among cognitive disorders; and (v) in identifying specific points of contact and mutual reinforcement between these two processes (self-domestication and early language evolution), including reduction in physical aggression and stress/tension, as well as sexual selection. (shrink)

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 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.

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, and in general this moment in the history of science, is calling for us linguists, and especially those of us who have worked in Minimalism, to characterize what it is that our approach has discovered, that we want to embrace and move forward with, and what it is that we need to discard. There is plenty in both categories, and it is precisely the considerations of biology (e.g. language evolution) that can help us weed out the burdensome, damaging (...) aspects of this approach. Too often we linguists look down upon the study of language evolution as some kind of marginal topic that need not concern “true” linguists, and we prefer to just wait until geneticists, biologists, and neuroscientists figure it all out. And yet, it is only linguists who can put forward specific, linguistically informed hypotheses that can be subjected to interdisciplinary testing. The emphasis here is on specific, falsifiable hypotheses, rather than some vague assertions that cannot be subjected to falsification. It is true that many such specific hypotheses will be proven wrong, but after all, the nature of the scientific process is simply to narrow down the range of possibilities. My focus here is on a few influential assumptions/postulates in Minimalism that are particularly harmful in establishing meaningful links between language and biology, and which, both on this ground, and based on more careful linguistic considerations, should be abandoned. I will also point to certain postulates... (shrink)

Broadly, the subject of this paper is the relation between logic and linguistics. More narrowly, it concentrates on formal semantics. The first part of the text discusses the topics and methods of formal semantics, and the second part the history of formal semantics. Formal semantic analysis has not been widely known and applied in our research community, and formal methods have been applied extremely rarely in linguistic analyses. This is why it is useful to point out the significant achievements of (...) formal semantics. This inspiring interdisciplinary field of research has been successfully connecting research in linguistics, logic and philosophy since the early 1970s. (shrink)

Tema je ovoga teksta u širem smislu osvrt na odnos logike i lingvistike. U užem smislu tekst će se u prvome dijelu osvrnuti na teme i instrumentarij, a u drugom na povijest formalne semantike. Recepcija formalnosemantičkih radova na našim područjima nema čvršću tradiciju, kao ni primjena formalnih metoda na proučavanje jezika, pa se i stoga čini korisnim ukazati na njezine dosege. Formalna semantika inspirativno je i plodonosno interdisciplinarno polje istraživanja koje je od 70-tih godina 20. stoljeća iznimno uspješno povezivalo istraživanja (...) lingvista, logičara i filozofa.Broadly, the subject of this paper is the relation between logic and linguistics. More narrowly, it concentrates on formal semantics. The first part of the text discusses the topics and methods of formal semantics, and the second part the history of formal semantics. Formal semantic analysis has not been widely known and applied in our research community, and formal methods have been applied extremely rarely in linguistic analyses. This is why it is useful to point out the significant achievements of formal semantics. This inspiring interdisciplinary field of research has been successfully connecting research in linguistics, logic and philosophy since the early 1970s. (shrink)

Business Ethics: A European Review, EarlyView.

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.

Care is at the heart of the Maori values system, which calls for humans to be kaitiaki, caretakers of the maun y the life-force, in each other and in nature. The relational Five Well-beings approach, based on four case studies of Maori businesses, demonstrates how business can create spiritual, cultural, social, environmental and economic well-being. A Well-beings approach entails praxis, which brings values and practice together with the purpose of consciously creating well-being and, in so doing, creates multi-dimensional wealth. Underlying (...) the Well-beings approach is an ethic of care and an intrinsic stakeholder view of business. (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.

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.

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 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.

We clarify some points previously made by Andrews, and defend the claim that Davidson's account of belief can be and is challenged by the existence of some people with autism. We argue that both Bouma and Andrews (Philosophical Psychology, 15) blurred the subtle distinctions between the psychological concepts of theory of mind and joint attention and the Davidsonian concepts of interpretation and triangulation. And we accept that appeal to control group studies is not the appropriate place to look for an (...) individual who can speak but who has significant problems with interpretation. In this paper we argue that by turning to the clinical literature we can more readily find such a challenge to Davidson's account. (shrink)

U poslednjih nekoliko dekada vise studija posvecenih percepciji novorodjencadi je ukazalo na to da cak i tek rodjena deca jesu osetljiva na nacin na koji se objekti pokrecu i na prirodu njihove interakcije. Da bi objasnili ranu pojavu ovakve osetljivosti na kauzalne odnose neki psiholozi zastupaju stanoviste da postoji urodjeno znanje vezano za objekte. Cilj ovog rada je da preispita ovakva nativisticka objasnjenja tako sto ce da preispita da li ova objasnjenja ispunjavaju uslove koji svaki mehanicisticki model mora da ispuni (...) da bi bio uspesan. Craver je razvio nekoliko takvih kriterijuma kao i distinkciju izmedju odgovarajuceg mehanicistickog modela i mehanicisticke skice. Moj cilj je da pokazem da nativisticki modeli razvoja ne ispunjavaju ove kriterijume. Prvo, ti modeli samo delimicno a ne u potpunosti opisuju fenomen. Drugo, nativisti ukljucuju u opis fenomena odredjenu teoriju percepcije koja zahteva dodatnu empirijsku evidenciju i ne moze biti bezrezervno prihvacena kao tacna. Ja cu takodje argumentovati da je urodjeno znanje dobar kandidat za ono sto Craver naziva?praznim terminom? i da ce najverovatnije biti napusten. Novija istrazivanja koja su ispitivala intersenzornu percepciju ukazuju na to da je mehanizam odgovoran za rano opazanje kauzalnih odnosa najverovatnije deo nase najosnovnije fiziologije i da kao takav ne ukljucuje sofisticirane kognitivne strukture niti urodjeno znanje. Takodje, ova istrazivanja ukazuju na to da je standardna debata izmedju nativista i empirista pogresno postavljena i da bi je trebalo napustiti. (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 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.

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)

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.

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)

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.

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)

S. Oyama’s prominent account of the Parity Thesis states that one cannot distinguish in a meaningful way between nature-based (i.e. gene-based) and nurture-based (i.e. environment-based) characteristics in development because the information necessary for the resulting characteristics is contained at both levels. Oyama as well as P. E. Griffiths and K. Stotz argue that the Parity Thesis has far-reaching implications for developmental psychology in that both nativist and interactionist developmental accounts of psychological capacities that presuppose a substantial nature/nurture dichotomy are inadequate. (...) We argue that well-motivated abandoning of the nature/nurture dichotomy, as advocated in converging versions of the Parity Thesis in biology, does not necessarily entail abandoning the distinction between biologically given abilities necessary for the development of higher psychological capacities and the learning process they enable. Thus, contrary to the claims of the aforementioned authors, developmental psychologists need not discard a substantial distinction between innate (biologically given) characteristics and those acquired by learning, even if they accept the Parity Thesis. We suggest a two-stage account of development: the first stage is maturational and involves interaction of genetic, epigenetic and environmental causes, resulting in the endogenous biological ‘machinery’ (e.g. language acquisition device), responsible for learning in the subsequent stage of the developmental process by determining the organism’s responses to the environment. This account retains the crux of nativism (the endogenous biological structure determines the way the organism learns/responds to an environment) whilst adopting the developmentalist view of biology by characterizing environments as distinctly different in terms of structure and function in two developmental stages. (shrink)

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)

According to the mental continuity claim (MCC), human mental faculties are physical and beneficial to human survival, so they must have evolved gradually from ancestral forms and we should expect to see their precursors across species. Materialism of mind coupled with Darwin’s evolutionary theory leads directly to such claims and even today arguments for animal mental properties are often presented with the MCC as a premise. However, the MCC has been often challenged among contemporary scholars. It is usually argued that (...) only humans use language and that language as such has no precursors in the animal kingdom. Moreover, language is quite often understood as a necessary tool for having representations and forming beliefs. As a consequence, by lacking language animals could not have developed representational systems or beliefs. In response to these worries, we aim to mount a limited defense of the MCC as an empirical hypothesis. First, we will provide a short historical overview of the origins of the MCC and examine some of the motives behind traditional arguments for and against it. Second, we will focus on one particular question, namely whether language as such is necessary for having beliefs. Our goal is to show that there is little reason to think language is necessary for belief. In doing so, we will challenge a view of belief that is widely accepted by those working in animal cognition, namely representational belief, and we will argue that if belief is non-representational, then different research questions and methods are required. We will conclude with an argument that to study the evolution of belief across species, it is essential to begin the study of subjects in their social and ecological environment rather than in contexts that are not ecologically valid along the social and ecological dimensions. Thus, rather than serving as a premise in an argument 3 in favor of animal minds, the MCC can only be defended by empirical investigation, but importantly, empirical investigation of the right sort.. (shrink)

The paper offers an argument against Kripke’s assertion, that it is valid for all names of natural species, that they have no connotations. The argumentation has is roots in the semantic conception of S. Kripke as articulated in his Naming and necessity. i.e., it is an „argument from inside“ the conception itself. The argument consists of two parts: setting the conditions under which the name of a natural species has a connotation; constructing a situation, in which these conditions are fulfilled.