In this paper we discuss the extent to which conjunction and disjunction can be rightfully regarded as such, in the context of infectious logics. Infectious logics are peculiar many-valued logics whose underlying algebra has an absorbing or infectious element, which is assigned to a compound formula whenever it is assigned to one of its components. To discuss these matters, we review the philosophical motivations for infectious logics due to Bochvar, Halldén, Fitting, Ferguson (...) and Beall, noticing that none of them discusses our main question. This is why we finally turn to the analysis of the truth-conditions for conjunction and disjunction in infectious logics, employing the framework of plurivalent logics, as discussed by Priest. In doing so, we arrive at the interesting conclusion that —in the context of infectious logics— conjunction is conjunction, whereas disjunction is not disjunction. (shrink)

Infectious logics are systems that have a truth-value that is assigned to a compound formula whenever it is assigned to one of its components. This paper studies four-valued infectious logics as the basis of transparent theories of truth. This take is motivated as a way to treat different pathological sentences differently, namely, by allowing some of them to be truth-value gluts and some others to be truth-value gaps and as a way to treat the semantic pathology (...) suffered by at least some of these sentences as infectious. This leads us to consider four distinct four-valued logics: one where truth-value gaps are infectious, but gluts are not; one where truth-value gluts are infectious, but gaps are not; and two logics where both gluts and gaps are infectious, in some sense. Additionally, we focus on the proof theory of these systems, by offering a discussion of two related topics. On the one hand, we prove some limitations regarding the possibility of providing standard Gentzen sequent calculi for these systems, by dualizing and extending some recent results for infectious logics. On the other hand, we provide sound and complete four-sided sequent calculi, arguing that the most important technical and philosophical features taken into account to usually prefer standard calculi are, indeed, enjoyed by the four-sided systems. (shrink)

The aim of this paper is to explore the peculiar case of infectious logics, a group of systems obtained generalizing the semantic behavior characteristic of the -fragment of the logics of nonsense, such as the ones due to Bochvar and Halldén, among others. Here, we extend these logics with classical negations, and we furthermore show that some of these extended systems can be properly regarded as logics of formal inconsistency and logics of formal undeterminedness.

This paper addresses the use of dispositions in the Infectious Disease Ontology (IDO). IDO is an ontology constructed according to the principles of the Open Biomedical Ontology (OBO) Foundry and uses the Basic Formal Ontology (BFO) as an upper ontology. After providing a brief introduction to disposition types in BFO and IDO, we discuss three general techniques for representing combinations of dispositions under the headings blocking dispositions, complementary dispositions, and collective dispositions. Motivating examples for each combination of dispositions is (...) given along with a specific use case in IDO. Description logic restrictions are used to formalize statements relating to these combinations. (shrink)

The first degree entailment (FDE) family is a group of logics, a many-valued semantics for each system of which is obtained from classical logic by adding to the classical truth-values true and false any subset of {both, neither, indeterminate}, where indeterminate is an infectious value (any formula containing a subformula with the value indeterminate itself has the value indeterminate). In this paper, we see how to extend a version of star semantics for the logics whose many-valued semantics (...) lack indeterminate to star semantics for logics whose many-valued semantics include indeterminate. The equivalence of the many-valued semantics and star semantics is established by way of a soundness and completeness proof. The upshot of the novel semantics in terms of the applied semantics of these logics, and specifically infectiousness, is explored, settling on the idea that infectiousness concerns ineffability. (shrink)

Logics based on weak Kleene algebra (WKA) and related structures have been recently proposed as a tool for reasoning about flaws in computer programs. The key element of this proposal is the presence, in WKA and related structures, of a non-classical truth-value that is “contaminating” in the sense that whenever the value is assigned to a formula ϕ, any complex formula in which ϕ appears is assigned that value as well. Under such interpretations, the contaminating states represent occurrences of (...) a flaw. However, since different programs and machines can interact with (or be nested into) one another, we need to account for different kind of errors, and this calls for an evaluation of systems with multiple contaminating values. In this paper, we make steps toward these evaluation systems by considering two logics, HYB1 and HYB2, whose semantic interpretations account for two contaminating values beside classical values 0 and 1. In particular, we provide two main formal contributions. First, we give a characterization of their relations of (multiple-conclusion) logical consequence—that is, necessary and sufficient conditions for a set Δ of formulas to logically follow from a set Γ of formulas in HYB1 or HYB2 . Second, we provide sound and complete sequent calculi for the two logics. (shrink)

We examine the set of formula-to-formula valid inferences of Classical Logic, where the premise and the conclusion share at least a propositional variable in common. We review the fact, already proved in the literature, that such a system is identical to the first-degree entailment fragment of R. Epstein's Relatedness Logic, and that it is a non-transitive logic of the sort investigated by S. Frankowski and others. Furthermore, we provide a semantics and a calculus for this logic. The semantics is defined (...) in terms of a \-matrix built on top of a 5-valued extension of the 3-element weak Kleene algebra, whereas the calculus is defined in terms of a Gentzen-style sequent system where the left and right negation rules are subject to linguistic constraints. (shrink)

The Covid-19 pandemic raises the need for an ethical framework addressing unique questions of airborne infectious disease. In particular, are you ethically obliged to wear a face mask? If so, why and when? The Respiratory Ethics Framework (REF) herein derives answers from ethical norms. Always covering coughs and sneezes just in case you might be infectious is an ethical norm. But if you are infectious with an airborne illness, you are probably spreading germs even with every breath (...) and vocalization. Therefore, given that respiratory covering should be done to prevent spreading germs, you should wear a mask if you believe you are infectious because it also provides covering while breathing and vocalizing. REF is grounded in the non-harm principle. Why should we avoid spreading infections to others? Because they can cause bodily physical harm and we should act to prevent causing such harm to others without justifiable reason. Under REF, the magnitude of your obligation to mask is proportional to the magnitude of risk you pose to others by way of airborne germs. This functional relationship is logically modeled and visually mapped with a decision matrix in this essay. (shrink)

This paper addresses a family of issues surrounding the biological phenomenon of resistance and its representation in realist ontologies. The treatments of resistance terms in various existing ontologies are examined and found to be either overly narrow, internally inconsistent, or otherwise problematic. We propose a more coherent characterization of resistance in terms of what we shall call blocking dispositions, which are collections of mutually coordinated dispositions which are of such a sort that they cannot undergo simultaneous realization within a single (...) bearer. A definition of ‘protective resistance’ is proposed for use in the Infectious Disease Ontology (IDO) and we show how this definition can be used to characterize the antibiotic resistance in Methicillin-Resistant Staphylococcus aureus (MRSA). The ontological relations between entities in our MRSA case study are used alongside a series of logical inference rules to illustrate logical reasoning about resistance. A description logic representation of blocking dispositions is also provided. We demonstrate that our characterization of resistance is sufficiently general to cover two other cases of resistance in the infectious disease domain involving HIV and malaria. (shrink)

This paper was written to study the order of medical advances throughout history. It investigates changing human beliefs concerning the causes of diseases, how modern surgery developed and improved methods of diagnosis and the use of medical statistics. Human beliefs about the causes of disease followed a logical progression from supernatural causes, such as the wrath of the Gods, to natural causes, involving imbalances within the human body. The invention of the microscope led to the discovery of microorganisms which were (...) eventually identified as the cause of infectious diseases. Identification of the particular microorganism causing a disease led to immunization against the disease. Modern surgery only developed after the ending of the taboo against human dissection and the discovery of modern anesthesia and the discovery of the need for anti-septic practices. Modern diagnostic practices began with the discovery of x-rays and the invention of medical scanners. Improved mathematics, especially in probability theory, led to statistical studies which led to a much greater ability, to identify the causes of disease, and to evaluate the effectiveness of treatments. These discoveries all occurred in a necessary and inevitable order with the easiest discoveries being made first and the harder discoveries being made later. The order of discovery determined the course of the history of medicine and is an example of how social and cultural history has to follow a particular course determined by the structure of the world around us. (shrink)

Technological developments have resulted in tremendous increases in the volume and diversity of the data and information that must be processed in the course of biomedical and clinical research and practice. Researchers are at the same time under ever greater pressure to share data and to take steps to ensure that data resources are interoperable. The use of ontologies to annotate data has proven successful in supporting these goals and in providing new possibilities for the automated processing of data and (...) information. In this chapter, we describe different types of vocabulary resources and emphasize those features of formal ontologies that make them most useful for computational applications. We describe current uses of ontologies and discuss future goals for ontology-based computing, focusing on its use in the field of infectious diseases. We review the largest and most widely used vocabulary resources relevant to the study of infectious diseases and conclude with a description of the Infectious Disease Ontology (IDO) suite of interoperable ontology modules that together cover the entire infectious disease domain. (shrink)

The Infectious Disease Ontology (IDO) is a suite of interoperable ontology modules that aims to provide coverage of all aspects of the infectious disease domain, including biomedical research, clinical care, and public health. IDO Core is designed to be a disease and pathogen neutral ontology, covering just those types of entities and relations that are relevant to infectious diseases generally. IDO Core is then extended by a collection of ontology modules focusing on specific diseases and pathogens. In (...) this paper we present applications of IDO Core within various areas of infectious disease research, together with an overview of all IDO extension ontologies and the methodology on the basis of which they are built. We also survey recent developments involving IDO, including the creation of IDO Virus; the Coronaviruses Infectious Disease Ontology (CIDO); and an extension of CIDO focused on COVID-19 (IDO-CovID-19).We also discuss how these ontologies might assist in information-driven efforts to deal with the ongoing COVID-19 pandemic, to accelerate data discovery in the early stages of future pandemics, and to promote reproducibility of infectious disease research. (shrink)

Background: Earlier study without actual trial indicated that caregivers needed delivery of information about outbreak situations independently of their job status. This report describes, for about two months in winter, actual delivery outbreak information to families with preschool children. The study objective was to confirm the usefulness of this information delivery. Method: Participants receiving outbreak information were recruited from the Child Care Support Service in a ward in Tokyo, Japan. Outbreak information was obtained from the Nursery School Absenteeism Surveillance System (...) (NSASSy) covering approximately 40% of all nursery schools in Japan, prescription surveillance and other resources. Delivery of outbreak information started in December 2017 and ceased at the end of February in 2018. After the delivery period, a questionnaire survey was administered to participants. Results: For this area, NSASSy showed the most dominant disease was influenza, with 707 patients, followed by group A streptococcal pharyngitis with 98 patients. The outbreak peak was inferred to be as Monday, 22 January, and it was announced by e-mail on 23 January. Of the 202 persons joined this trial, 60 participants responded to the questionnaire survey after the delivery period. Of those respondents, 98% wanted delivery of that information to continue. Conclusion: We found that almost all respondents confirmed usefulness of the information about infectious diseases which was delivered. (shrink)

A repository of clinically associated Staphylococcus aureus (Sa) isolates is used to semi‐automatically generate a set of application ontologies for specific subfamilies of Sa‐related disease. Each such application ontology is compatible with the Infectious Disease Ontology (IDO) and uses resources from the Open Biomedical Ontology (OBO) Foundry. The set of application ontologies forms a lattice structure beneath the IDO‐Core and IDO‐extension reference ontologies. We show how this lattice can be used to define a strategy for the construction of a (...) new taxonomy of infectious disease incorporating genetic, molecular, and clinical data. We also outline how faceted browsing and query of annotated data is supported using a lattice application ontology. (shrink)

On May 16, 2020, the Center for Academic Research and Training in Anthropogeny organized the symposium “Impact of Infectious Disease on Humans and Our Origins”. The symposium aimed to gather experts on infectious diseases in one place and discuss the interrelationship between different pathogens and humans in an evolutionary context. The talks discussed topics including SARS-CoV-2, dengue and Zika, the notion of human-specific diseases, streptococci, microbiome in the human reproductive tract, Salmonella enterica, malaria, and human immunological memory.

The global pandemic of COVID 19 has changed consumer behaviour to reduce the risk. This is common for all interpersonal interactions of individuals especially in maintaining the recommended interpersonal distance based on the recommendations from the health experts. Sri Lanka as a developing country affected by COVID 19, observed changes in individuals' day today’ consumption decision making due to pandemic. Importantly the retailing sector is highly influenced by the conditions since the frequency of interpersonal interactions and degree of interaction is (...) higher in the retailing sector. Interestingly the retailing sector with its largest contributor, the SMEs need to identify the unique changes that happen to the consumer behaviour in responding to them. Accordingly, the objective of the study is to examine the impact of infectious disease risk on the perceived retail crowding in two perspectives of human density and the spatial density. The study has used a quantitative survey in collecting data with the online self-administrated questionnaire with a sample of 100 consumers. Data analysis has been done by using a PLS-SEM with the support of SmartPLS version 3. The key findings of the study emphasize the significant positive influence of infectious disease risk on human density as well as on the spatial density. Based on the findings the study attempts to provide the implications for the retailing industry to cope with situational changes in the environment. (shrink)

Logic arguably plays a role in the normativity of reasoning. In particular, there are plausible norms of belief/disbelief whose antecedents are constituted by claims about what follows from what. But is logic also relevant to the normativity of agnostic attitudes? The question here is whether logical entailment also puts constraints on what kinds of things one can suspend judgment about. In this paper I address that question and I give a positive answer to it. In particular, I advance two logical (...) norms of agnosticism, where the first one allows us to assess situations in which the subject is agnostic about the conclusion of a valid argument and the second one allows us to assess situations in which the subject is agnostic about one of the premises of a valid argument. (shrink)

I argue against inferentialism about logic. First, I argue against an analogy between logic and chess, before considering a more basic objection to stipulating inference rules as a way of establishing the meaning of logical constants. The objectionthe Mushroom Omelette Objectionis that stipulative acts are partly constituted by logical notions, and therefore cannot be used to explain logical thought. I then argue that the same problem also attaches to following existing conventional rules, since either those rules have logical contents, or (...) following those conventional rules is done for logical reasons. Lastly, I compare this argument with other arguments found in Quine’s early work, and consider two attempts to reply to Quine. (shrink)

Overview of fundamental work in deontic logic.

The Logic of Analogy is a study of the valid logical forms of qualitative and quantitative analogical argument, and the rules pertaining to them. It investigates equally valid conflicting arguments, statistics-based arguments and their utility in science, arguments from precedent used in law-making or law-application, and examines subsumption in analogical terms. Included for purposes of illustration is a large section on Talmudic use of analogical reasoning.

The logical interpretation of probability, or "objective Bayesianism'' – the theory that (some) probabilities are strictly logical degrees of partial implication – is defended. The main argument against it is that it requires the assignment of prior probabilities, and that any attempt to determine them by symmetry via a "principle of insufficient reason" inevitably leads to paradox. Three replies are advanced: that priors are imprecise or of little weight, so that disagreement about them does not matter, within limits; that it (...) is possible to distinguish reasonable from unreasonable priors on logical grounds; and that in real cases disagreement about priors can usually be explained by differences in the background information. It is argued also that proponents of alternative conceptions of probability, such as frequentists, Bayesians and Popperians, are unable to avoid committing themselves to the basic principles of logical probability. (shrink)

This paper has two objectives 1) to study the influence of digital and new technology on COVID-19 diagnosis and healthcare 2) To propose the integral guideline solutions of the infectious disease for the future. COVID-19 stands for corona (CO), virus (VI), disease (D), or SARS-CoV-2, is a respiratory virus first identified in December 2019 in Wuhan, China(WHO, 2019). It is an epidemiological crisis that caused the deaths and sudden destruction of wealth and health of people around the world. Many (...) countries responded to the crisis with what could only be called urgent prevention and treatment. In the 21st century, our society is based on digital and new technology that can control and prevent the COVID-19 pandemics. However, these ways for solving the problem of COVID-19 pandemics are rising an epistemological crisis too. There are some problems with the COVID-19 diagnosis. From Buddhist philosophy perspective, COVID-19 teaches us the coronavirus is causing us to experience some heightened forms of the three marks of our existence which are the impermanence (aniccā), the suffering (duḥkha), and the non-self (anatta). The establishment of scientific expertise and innovation has shown its value and educating the public about testing, diagnosis, communication, treatment, and vaccine development technology for prevention the of infectious diseases in the future. (shrink)

Current COVID-19 pandemic and previous SARS/MERS outbreaks have caused a series of major crises to global public health. We must integrate the large and exponentially growing amount of heterogeneous coronavirus data to better understand coronaviruses and associated disease mechanisms, in the interest of developing effective and safe vaccines and drugs. Ontologies have emerged to play an important role in standard knowledge and data representation, integration, sharing, and analysis. We have initiated the development of the community-based Coronavirus Infectious Disease Ontology (...) (CIDO). As an Open Biomedical Ontology (OBO) library ontology, CIDO is an open source and interoperable with other existing OBO ontologies. In this article, the general architecture and the design patterns of the CIDO are introduced, CIDO representation of coronaviruses, phenotypes, anti-coronavirus drugs and medical devices (e.g. ventilators) are illustrated, and an application of CIDO implemented to identify repurposable drug candidates for effective and safe COVID-19 treatment is presented. (shrink)

Plants from a handful of species provide the primary source of food for all people, yet this source is vulnerable to multiple stressors, such as disease, drought, and nutrient deficiency. With rapid population growth and climate uncertainty, the need to produce crops that can tolerate or resist plant stressors is more crucial than ever. Traditional plant breeding methods may not be sufficient to overcome this challenge, and methods such as highOthroughput sequencing and automated scoring of phenotypes can provide significant new (...) insights. Ontologies are essential tools for accessing and analysing the large quantities of data that come with these newer methods. As part of a larger project to develop ontologies that describe plant phenotypes and stresses, we are developing a plant disease extension of the Infectious Disease Ontology (IDOPlant). The IDOPlant is envisioned as a reference ontology designed to cover any plant infectious disease. In addition to novel terms for infectious diseases, IDOPlant includes terms imported from other ontologies that describe plants, pathogens, and vectors, the geographic location and ecology of diseases and hosts, and molecular functions and interactions of hosts and pathogens. To encompass this range of data, we are suggesting inOhouse ontology development complemented with reuse of terms from orthogonal ontologies developed as part of the Open Biomedical Ontologies (OBO) Foundry. The study of plant diseases provides an example of how an ontological framework can be used to model complex biological phenomena such as plant disease, and how plant infectious diseases differ from, and are similar to, infectious diseases in other organism. (shrink)

This book explores the idea that all of logic can be reduced to two very simple rules that are sensitive to logical polarity. The authors show that this idea has profound consequences for our understanding of the nature of human inferential capacities, and for some of the key issues in contemporary linguistics.

The main research goal of the work is to study the notion of co-topos, its correctness, properties and relations with toposes. In particular, the dualization process proposed by proponents of co-toposes has been analyzed, which transforms certain Heyting algebras of toposes into co-Heyting ones, by which a kind of paraconsistent logic may appear in place of intuitionistic logic. It has been shown that if certain two definitions of topos are to be equivalent, then in one of them, in the context (...) of a subobject classifier, there should be a neutral label for the generic subobject, or if the label "true" appears instead, it carries no additional properties or assumptions. It has been shown that a natural isomorphism occurring in one of the definitions of topos need not be an isomorphism of the corresponding algebraic structures on the sets, so that a co-Heyting algebraic structure can be defined on the set of characteristic morphisms, which moreover will also be natural. The analyzes suggest that the notion of co-topos may be considered correct. However, it should be strongly emphasized that although the possibility of defining the notion of co-topos has been shown, its further full consequences should be very carefully examined, which can severely limit its logical applications. (shrink)

Buddhist philosophers have developed a rich tradition of logic. Buddhist material on logic that forms the Buddhist tradition of logic, however, is hardly discussed or even known. This article presents some of that material in a manner that is accessible to contemporary logicians and philosophers of logic and sets agendas for global philosophy of logic.

This work aims to make tense logic a more robust tool for ontologists, philosophers, knowledge engineers and programmers by outlining a fusion of tense logic and ontology of time. In order to make tense logic better understandable, the central formal primitives of standard tense logic are derived as theorems from an informal and intuitive ontology of time. In order to make formulation of temporal propositions easier, temporal operators that were introduced by Georg Henrik von Wright are developed, and mapped to (...) the ontology of time. (shrink)

A natural suggestion and increasingly popular account of how to revise our logical beliefs treats revision of logic analogously to the revision of scientific theories. I investigate this approach and argue that simple applications of abductive methodology to logic result in revision-cycles, developing a detailed case study of an actual dispute with this property. This is problematic if we take abductive methodology to provide justification for revising our logical framework. I then generalize the case study, pointing to similarities with more (...) recent and popular heterodox logics such as naïve logics of truth. I use this discussion to motivate a constraint—logical partisanhood—on the uses of such methodology: roughly: both the proposed alternative and our actual background logic must be able to agree that moving to the alternative logic is no worse than staying put. (shrink)

Logical information theory is the quantitative version of the logic of partitions just as logical probability theory is the quantitative version of the dual Boolean logic of subsets. The resulting notion of information is about distinctions, differences and distinguishability and is formalized using the distinctions of a partition. All the definitions of simple, joint, conditional and mutual entropy of Shannon information theory are derived by a uniform transformation from the corresponding definitions at the logical level. The purpose of this paper (...) is to give the direct generalization to quantum logical information theory that similarly focuses on the pairs of eigenstates distinguished by an observable, i.e., qudits of an observable. The fundamental theorem for quantum logical entropy and measurement establishes a direct quantitative connection between the increase in quantum logical entropy due to a projective measurement and the eigenstates that are distinguished by the measurement. Both the classical and quantum versions of logical entropy have simple interpretations as “two-draw” probabilities for distinctions. The conclusion is that quantum logical entropy is the simple and natural notion of information for quantum information theory focusing on the distinguishing of quantum states. (shrink)

Inductive Logic is a ‘thematic compilation’ by Avi Sion. It collects in one volume many (though not all) of the essays, that he has written on this subject over a period of some 23 years, which all demonstrate the possibility and conditions of validity of human knowledge, the utility and reliability of human cognitive means when properly used, contrary to the skeptical assumptions that are nowadays fashionable. A new essay, The Logic of Analogy, was added in 2022.

Logical Criticism of Buddhist Doctrines is a ‘thematic compilation’ by Avi Sion. It collects in one volume the essays that he has written on this subject over a period of some 15 years after the publication of his first book on Buddhism, Buddhist Illogic. It comprises expositions and empirical and logical critiques of many (though not all) Buddhist doctrines, such as impermanence, interdependence, emptiness, the denial of self or soul. It includes his most recent essay, regarding the five skandhas doctrine.

One of the open problems in the philosophy of information is whether there is an information logic (IL), different from epistemic (EL) and doxastic logic (DL), which formalises the relation “a is informed that p” (Iap) satisfactorily. In this paper, the problem is solved by arguing that the axiom schemata of the normal modal logic (NML) KTB (also known as B or Br or Brouwer’s system) are well suited to formalise the relation of “being informed”. After having shown that IL (...) can be constructed as an informational reading of KTB, four consequences of a KTB-based IL are explored: information overload; the veridicality thesis (Iap → p); the relation between IL and EL; and the Kp → Bp principle or entailment property, according to which knowledge implies belief. Although these issues are discussed later in the article, they are the motivations behind the development of IL. (shrink)

Antimicrobial resistance (AMR) is a global public health disaster driven largely by antibiotic use in human health care. Doctors considering whether to prescribe antibiotics face an ethical conflict between upholding individual patient health and advancing public health aims. Existing literature mainly examines whether patients awaiting consultations desire or expect to receive antibiotic prescriptions, but does not report views of the wider public regarding conditions under which doctors should prescribe antibiotics. It also does not explore the ethical significance of public views (...) or their sensitivity to awareness of AMR risks or the standpoint (self-interested or impartial) taken by participants. Methods: An online survey was conducted with a sample of the U.S. public (n = 158). Participants were asked to indicate what relative priority should be given to individual patients and society-at-large from various standpoints and in various contexts, including antibiotic prescription. Results: Of the participants, 50.3% thought that doctors should generally prioritize individual patients over society, whereas 32.0% prioritized society over individual patients. When asked in the context of AMR, 39.2% prioritized individuals whereas 45.5% prioritized society. Participants were significantly less willing to prioritize society over individuals when they themselves were the patient, both in general (p = .001) and in relation to AMR specifically (p = .006). Conclusions: Participants’ attitudes were more oriented to society and sensitive to collective responsibility when informed about the social costs of antibiotic use and when considered from a third-person rather than first-person perspective. That is, as participants came closer to taking the perspective of an informed and impartial “ideal observer,” their support for prioritizing society increased. Our findings suggest that, insofar as antibiotic policies and practices should be informed by attitudes that are impartial and well-informed, there is significant support for prioritizing society. (shrink)

Buddhist philosophers have investigated the techniques and methodologies of debate and argumentation which are important aspects of Buddhist intellectual life. This was particularly the case in India, where Buddhism and Buddhist philosophy originated. But these investigations have also engaged philosophers in China, Japan, Korea and Tibet, and many other parts of the world that have been influenced by Buddhism and Buddhist philosophy. Several elements of the Buddhist tradition of philosophy are thought to be part of this investigation. -/- There are (...) interesting reasoning patterns discernible in the writings of Buddhist philosophers. For instance, the Mādhyamika philosopher Nāgārjuna presents arguments for the emptiness of all things in terms of catuṣkoṭi (four ‘corners’: roughly speaking, truth, false, both, neither). There are also the Indian vāda (debate) literature and Tibetan bsdus grwa (collected topics) that list techniques of debates. -/- The main interest here is the tradition of Buddhist philosophy, sometimes referred to as Pramāṇavāda, whose central figures are Dignāga (approx. 480–540 CE) and Dharmakīrti (6th– 7th CE). This philosophy is understood to be the Buddhist school of logic-epistemology. ‘Pramāṇavāda’ is not a doxographical term traditionally used to refer to a recognised school of Buddhist philosophy. It is a conventional term that is sometimes used in modern literature. Nevertheless, in what follows, we think of it as a tradition within Buddhist philosophy and ‘Buddhist logic’ refers to what is developed in this tradition. -/- Buddhist logicians have systematically analysed the kind of reasoning involved in acquiring knowledge. They hold that there are valid ways to reason that are productive of knowledge. In what follows, some of the main elements of their analyses will be described. Note, however, that, while exegetical studies of Buddhist texts are important, we must step back from them and consider what is involved in taking a Buddhist approach to logic in light of modern formal logic. This analysis will be done against the backdrop of the contemporary literature on logic and related subjects in contemporary philosophy to make sense of the logical studies by Buddhist logicians. (shrink)

Logic in the Torah is a ‘thematic compilation’ by Avi Sion. It collects in one volume essays that he has written on this subject in Judaic Logic (1995) and A Fortiori Logic (2013), in which traces of logic in the Torah and related religious documents (the Nakh, the Christian Bible, and the Koran and Hadiths) are identified and analyzed.

Logic in the Talmud is a ‘thematic compilation’ by Avi Sion. It collects in one volume essays that he has written on this subject in Judaic Logic (1995) and A Fortiori Logic (2013), in which traces of logic in the Talmud (the Mishna and Gemara) are identified and analyzed. While this book does not constitute an exhaustive study of logic in the Talmud, it is a ground-breaking and extensive study. A new essay, The Logic of Analogy, was added in 2022.

I argue that we can and should extend Tarski's model-theoretic criterion of logicality to cover indefinite expressions like Hilbert's ɛ operator, Russell's indefinite description operator η, and abstraction operators like 'the number of'. I draw on this extension to discuss the logical status of both abstraction operators and abstraction principles.

Scholars have argued that Plato's decision to include women in the ruling class was either intended as a joke, or else was forced on him by other political commitments. In tis paper, I argue that the arguments he offers for including women in positions of power can and should be taken as sincere.

A central tenet of medical ethics holds that it is permissible to perform a medical intervention on a competent individual only if that individual has given informed consent to the intervention. However, in some circumstances it is tempting to say that the moral reason to obtain informed consent prior to administering a medical intervention is outweighed. For example, if an individual’s refusal to undergo a medical intervention would lead to the transmission of a dangerous infectious disease to other members (...) of the community, one might claim that it would be morally permissible to administer the intervention even in the absence of consent. Indeed, as we shall discuss below, there are a number of examples of public health authorities implementing compulsory or coercive measures for the purposes of infectious disease control (IDC). The plausibility of the thought that non-consensual medical interventions might be justified when performed for the purpose of IDC raises the question of whether such interventions might permissibly be used to realize other public goods. In this article we focus on one possibility: whether it could be permissible to non-consensually impose certain interventions that alter brain states or processes through chemical or physical means on serious criminal offenders. We shall suggest that some such interventions might be permissible if they safely and effectively serve to facilitate the offender’s rehabilitation and thereby prevent criminal recidivism. (shrink)

Rapidly, accurately and easily interpreting generated data is of fundamental concern. Ontologies – structured controlled vocabularies – support interoperability and prevent the development of data silos which undermine interoperability. The Open Biological and Biomedical Ontologies (OBO) Foundry serves to ensure ontologies remain interoperable through adherence by its members to core ontology design principles. For example, the Infectious Disease Ontology (IDO) Core includes terminological content common to investigations of all infectious diseases. Ontologies covering more specific infectious diseases in (...) turn extend from IDOCore, such as the Coronavirus Infectious Disease Ontology (CIDO). The growing list of virus-specific IDO extensions has motivated construction of a reference ontology covering content common to viral infectious disease investigations: the Virus Infectious Disease Ontology (VIDO). Additionally the present pandemic has motivated construction of a more specific extension of CIDO covering terminological contents specific to the pandemic: the COVID-19 Infectious Disease Ontology (IDO-COVID-19). We report here the development of VIDO and IDO-COVID-19. More specifically we examine newly minted terms for each ontology, showcase reuse of terms from existing OBO ontologies, motivate choicepoints for ontological decisions based on research from relevant life sciences, apply ontology terms to explicate viral pathogenesis, and discuss the annotating power of virus ontologies for use in machine-learning projects. (shrink)

We analyze the logical form of the domain knowledge that grounds analogical inferences and generalizations from a single instance. The form of the assumptions which justify analogies is given schematically as the "determination rule", so called because it expresses the relation of one set of variables determining the values of another set. The determination relation is a logical generalization of the different types of dependency relations defined in database theory. Specifically, we define determination as a relation between schemata of first (...) order logic that have two kinds of free variables: (1) object variables and (2) what we call "polar" variables, which hold the place of truth values. Determination rules facilitate sound rule inference and valid conclusions projected by analogy from single instances, without implying what the conclusion should be prior to an inspection of the instance. They also provide a way to specify what information is sufficiently relevant to decide a question, prior to knowledge of the answer to the question. (shrink)

In the *Science of Logic*, Hegel states unequivocally that the category of “life” is a strictly logical, or pure, form of thinking. His treatment of actual life – i.e., that which empirically constitutes nature – arises first in his *Philosophy of Nature* when the logic is applied under the conditions of space and time. Nevertheless, many commentators find Hegel’s development of this category as a purely logical one especially difficult to accept. Indeed, they find this development only comprehensible as long (...) as one simultaneously assumes that Hegel breaks his promise to let the logic do the leading. However, if Hegel were to in fact allow the logical development to be led by biological analogies at this point, problems would ensue. Not only would it contradict his own speculative method, which should secure the necessity of the categories, but it would also endanger the ontological generality of the category of life itself. Beyond undermining his method and the logical integrity of the category, however, I will argue that such a reading makes the transition to the next category of “cognition” unintelligible and problematic. My aim in the first part of this paper is to argue how logical life can be read as a pure category. I then argue in the second part how my reconstruction makes the transition to cognition intelligible without resorting to profane or supernatural interpretations. (shrink)

An introductory textbook on metalogic. It covers naive set theory, first-order logic, sequent calculus and natural deduction, the completeness, compactness, and Löwenheim-Skolem theorems, Turing machines, and the undecidability of the halting problem and of first-order logic. The audience is undergraduate students with some background in formal logic.

Paraconsistent logics are logical systems that reject the classical principle, usually dubbed Explosion, that a contradiction implies everything. However, the received view about paraconsistency focuses only the inferential version of Explosion, which is concerned with formulae, thereby overlooking other possible accounts. In this paper, we propose to focus, additionally, on a meta-inferential version of Explosion, i.e. which is concerned with inferences or sequents. In doing so, we will offer a new characterization of paraconsistency by means of which a logic (...) is paraconsistent if it invalidates either the inferential or the meta-inferential notion of Explosion. We show the non-triviality of this criterion by discussing a number of logics. On the one hand, logics which validate and invalidate both versions of Explosion, such as classical logic and Asenjo–Priest’s 3-valued logic LP. On the other hand, logics which validate one version of Explosion but not the other, such as the substructural logics TS and ST, introduced by Malinowski and Cobreros, Egré, Ripley and van Rooij, which are obtained via Malinowski’s and Frankowski’s q- and p-matrices, respectively. (shrink)

According to traditional logical expressivism, logical operators allow speakers to explicitly endorse claims that are already implicitly endorsed in their discursive practice — endorsed in virtue of that practice’s having instituted certain logical relations. Here, I propose a different version of logical expressivism, according to which the expressive role of logical operators is explained without invoking logical relations at all, but instead in terms of the expression of discursive-practical attitudes. In defense of this alternative, I present a deflationary account of (...) the expressive role of vocabulary by which we ascribe logical relations. (shrink)

Logic and psychology overlap in judgment, inference and proof. The problems raised by this commonality are notoriously difficult, both from a historical and from a philosophical point of view. Sundholm has for a long time addressed these issues. His beautiful piece of work [A Century of Inference: 1837-1936] begins by summarizing the main difficulty in the usual provocative manner of the author: one can start, he says, by the act of knowledge to go to the object, as the Idealist does; (...) one can also start by the object to go to the act, in the Realist mood; never the two shall meet. He is himself inclined to accept the first perspective as the right one and he has eventually developed an original version of antirealism which starts, not from considerations about the publicity of meaning, in the manner of Dummett, but from an epistemic standpoint, trying to search in a non-Fregean tradition of analysis of judgement and cognate notions a way of founding constructivist semantics. The present paper ploughes the same field. We concentrate on the significance, for Sundholm’s program, of the perspective that has been opened by Twardowski in his important essay on acts and products (1912. (shrink)

Structuralism has recently moved center stage in philosophy of mathematics. One of the issues discussed is the underlying logic of mathematical structuralism. In this paper, I want to look at the dual question, namely the underlying structures of logic. Indeed, from a mathematical structuralist standpoint, it makes perfect sense to try to identify the abstract structures underlying logic. We claim that one answer to this question is provided by categorical logic. In fact, we claim that the latter can be seen—and (...) probably should be seen—as being a structuralist approach to logic and it is from this angle that categorical logic is best understood. (shrink)

In this thesis we present two logical systems, $\bf MP$ and $\MP$, for the purpose of reasoning about knowledge and effort. These logical systems will be interpreted in a spatial context and therefore, the abstract concepts of knowledge and effort will be defined by concrete mathematical concepts.

The notion of strength has featured prominently in recent debates about abductivism in the epistemology of logic. Following Williamson and Russell, we distinguish between logical and scientific strength and discuss the limits of the characterizations they employ. We then suggest understanding logical strength in terms of interpretability strength and scientific strength as a special case of logical strength. We present applications of the resulting notions to comparisons between logics in the traditional sense and mathematical theories.