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.

In this work, we propose a variant of so-called informational semantics, a technique elaborated by Voishvillo, for two infectious logics, Deutsch’s |${\mathbf{S}_{\mathbf{fde}}}$| and Szmuc’s |$\mathbf{dS}_{\mathbf{fde}}$|⁠. We show how the machinery of informational semantics can be effectively used to analyse truth and falsity conditions of disjunction and conjunction. Using this technique, it is possible to claim that disjunction and conjunction can be rightfully regarded as such, a claim which was disputed in the recent literature. Both |${\mathbf{S}_{\mathbf{fde}}}$| and |$\mathbf{dS}_{\mathbf{fde}}$| are (...) formalized in terms of natural deduction. This allows us to solve several problems: to develop a natural deduction calculus for |${\mathbf{S}_{\mathbf{fde}}}$| containing the standard form of disjunction elimination (in contrast to the calculus by Petrukhin), to introduce the first natural deduction calculus for |$\mathbf{dS}_{\mathbf{fde}}$| and to reflect the fundamental symmetry between |${\mathbf{S}_{\mathbf{fde}}}$| and |$\mathbf{dS}_{\mathbf{fde}}$| on proof-theoretical level forming a convenient basis for obtaining their well-known extensions |$\mathbf{K}^{\mathbf{w}}_{\mathbf{3}}$| and |$\mathbf{PWK}$|⁠. (shrink)

In this paper, we study logical systems which represent entailment relations of two kinds. We extend the approach of finding ‘exactly true’ and ‘non-falsity’ versions of four-valued logics that emerged in series of recent works [Pietz & Rivieccio (2013). Nothing but the truth. Journal of Philosophical Logic, 42(1), 125–135; Shramko (2019). Dual-Belnap logic and anything but falsehood. Journal of Logics and their Applications, 6, 413–433; Shramko et al. (2017). First-degree entailment and its relatives. Studia Logica, 105(6), 1291–1317] to (...) the case of infectious logics, namely to the case of Deutsch's logic Sfde introduced in Deutsch [Relevant analytic entailment. The Relevance Logic Newsletter, 2(1), 26–44; The completeness of S. Studia Logica, 38(2), 137–147]. The particular systems obtained in this way are Setl and Snfl. We present them in the form of sequent calculi and prove corresponding soundness and completeness theorems. We illuminate the connection between Setl, Snfl and two well-known systems, strong Kleene three-valued logic K3 and Priest's Logic of Paradox LP. This connection allows us to investigate the characterisation of the entailment relations associated with Setl and Snfl as well as to introduce the notion of ‘infectious analogue’ of a certain logic. We also study implicative extensions of Setl and Snfl and prove soundness and completeness theorems for them as well. (shrink)

Emotivists like Ayer claim that moral sentences are devoid of cognitive meaning since they only evince attitudinal approval or disapproval of actions. In this paper, I explore two non-classical sem...

Da Ré and Szmuc argue that while there is a symmetry between ‘infectious’ and ‘immune’ logics, this symmetry fails w.r.t. extending an algebra with an immune or an infectious element. In this paper, I show that the symmetry also fails w.r.t. defining a new logical operation from a given set of primitive (Boolean) operations. I use the case of the material conditional to illustrate this point.

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)

This article is concerned with an exploration of a family of systems—called immune logics—that arise from certain dualizations of the well-known family of infectious logics. The distinctive feature of the semantic of infectious logics is the presence of a certain “infectious” semantic value, by which two different though equivalent things are meant. On the one hand, it is meant that these values are zero elements for all the operations in the underlying algebraic structure. On (...) the other hand, it is meant that these values behave in a value-in-value-out fashion for all the operations in the underlying algebraic structure. Thus, in a rather informal manner, we will refer to immune logics as those systems whose underlying semantics count with a certain “immune” semantic value behaving in a way that is somewhat dual to that of the infectious values. In a more formal manner, carrying out this dualization will prove to be not as straightforward as one could imagine, since the two characterizations of infectiousness discussed above lead to two different outcomes when one tries to conduct them. We explore these alternatives and provide technical results regarding them, and the various logical systems defined using such semantics. (shrink)

Logics of significance have been proposed in an attempt to overcome the shortcomings of classical logic as a model of reasoning in the presence of nonsignificant (e.g., meaningless, ill-formed, unverifiable) sentences. Many-valued logicians have addressed this problem by introducing logics with infectious truth values. Cases in point are the weak Kleene logics B3 (paracomplete weak Kleene logic) and PWK (paraconsistent weak Kleene logic). Over time, it has become clear that the valid entailments of these significance (...) class='Hi'>logics obey variable inclusion patterns that link them to other, usually better known, logics—such patterns, however, allow for disturbing exceptions. Logics of pure (left or right) variable inclusion have been introduced with an eye to removing these exceptions. In this paper, we consider the pure left variable inclusion companion of classical logic and give a complete description of its subclassical extensions. We also provide relative axiomatizations and characteristic (sets of) matrices for each one of these extensions, as well as syntactic descriptions (in terms of variable inclusion criteria) for the valid entailments of some of them, and determine in each case the algebra reducts of the Suszko-reduced matrix models. (shrink)

In this article, we explore the semantic characterization of the (right) pure refined variable inclusion companion of all logics, which is a further refinement of the nowadays well-studied pure right variable inclusion logics. In particular, we will focus on giving a characterization of these fragments via a single logical matrix, when possible, and via a class of finite matrices, otherwise. In order to achieve this, we will rely on extending the semantics of the logics whose companions we (...) will be discussing with infectious values in direct and in more subtle ways. This further establishes the connection between infectious logics and variable inclusion logics. (shrink)

The paper presents the semantic model of logical content processing in the environment of tabooed sentences. Such sentences occur both in academic and colloquial discourses. They can be interpreted as infected formulas with the value of an insult. The proposed model assumes that the inferential mechanism of argumentative activities realised in discourses in the environment of such formulas is based on Bochvar's logical matrices and Kripke’s possible worlds semantic structures. This mechanism is determined by semantic consequence operators of three types. (...) The presented theory can be viewed as a formal tool for reconstructing the logical mental mechanism which stops deductive actions aiming at the development of narrative worlds in discourse practices during epistemic wars. It postulates that these practices, which occur in processes of developing science, are governed by special logical mechanisms of inference. (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)

This paper presents a weak Kleene approach to conditionals that preserves some salient formal features of conditionals, particularly their interdefinability with Boolean logical connectives. I argue that such an approach fares better than other proposed weak logics of conditionals in this regard. In particular, it fares better than the logics proposed by Cooper, Cantwell, Farrell, De Finetti, Égré, Rossi, and Sprenger.

In one of his papers, JC Beall advanced a new and interesting interpretation of Weak Kleene logic, in terms of on-topic/off-topic. In brief, Beall suggests to read the third value as _off-topic_, whereas the two classical values are read as _true and on-topic_ and _false and on-topic_. Building on Beall’s new interpretation, the aim of this paper is threefold. First, we discuss two motivations to enrich Beall’s interpretation, and offer an alternative semantic framework that reflects our motivations. Second, by making (...) use of our new framework, we will offer a new interpretation of the logic of Catuskoti which combines Beall’s proposal of having _FDE_ as the correct logic with the on-topic/off-topic divide. Finally, we will offer a general result that will allow us to make sense of a family of infectious logics in terms of Beall’s on-topic/off-topic reading. (shrink)

Examining the Danish poultry industry in a time of rising outbreaks of infectious disease (the so-called ‘pandemic era’) including avian influenza, this study documents the often-unseen harms resulting from current dominant forms of response. Inspired by multispecies studies and ethnography, we pay attention to entangled human and more-than-human worlds. Specifically, we document the multifarious ways in which responses to worsening avian influenza alter the everyday lives of birds in production, their farmers, and public veterinarians. We also show how such (...) changes are distributed in ways that further slant the playing field against smaller scale and organic poultry production, under the hegemony of globalized capitalist agriculture. Throughout, we shed light on the analytical purchase of two key concepts in feminist scholarship and science and technology studies respectively: care and repair. While understood as integral to human and more-than-human wellbeing, care’s tendency to summon pleasant associations is challenged by the reality of embodied care practices in complex and compromised socio-ecological contexts. Repair has been wielded conceptually to interrogate activities that stabilize systems at risk, while largely ignoring or even exacerbating the drivers of instability. Mobilized together, we can better understand how hegemonic logics delimit possibilities for care, but also the limits and limitations of dominant response repertoires. Finally, we illuminate farming practices of care beyond repair, which may help chart alternatives for Danish agriculture within, and perhaps beyond, the pandemic era. (shrink)

This article tackles an old, classical problem, which is acquiring a new epochal relevance with the techno-aesthetic processing of form and substance, expression and content. The field of digital architecture is embarked in the ancient controversy between the line and the curve, binary communication and fuzzy logic. Since the 1990s, the speculative qualities of digital architecture have exposed spatial design to the qualities of growing or breeding, rather than planning. However, such qualities still deploy the tension between discrete spaces and (...) continual curving. In this context, the article suggests the computational coexistence of discrete coding with continual morphing, defying any easy resolution for an aesthetic of continuity or discontinuity, the superiority of the analog or the meta-logic of the digital. The metaphysical dimension of such coexistence needs to include the abstract capacities of experiencing the transition from one state to another as the registering of algorithmic processing. Computation is intrinsic to microperceptions, incomputable quantities deploying the infectious property of the digital code. The article draws on the digital architecture of Greg Lynn to explore whether the computational nature of the digital calculus has the potential to challenge the bifurcation between the biological and the mathematical, the physical and the mental. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:An Epidemic of Difficult PatientsKeva SouthwellAs the opioid epidemic marches on, we have all become familiar with a particular breed of "difficult patient," the intravenous drug user. Most teams try to get through these admissions with as few interactions as possible. Nurses will tell you how much they hate caring for these patients, often citing "they did this to themselves" as they experience prolonged admissions due to infections resulting (...) from Intravenous Drug Use (IVDU). Most services try to get out of admitting these patients, saying they are more appropriate with infectious disease, cardiology, or "anywhere but with me." These patients often use drugs in the hospital, threaten to leave AMA, and are dangerous, liable to assault or abuse the very staff trying to help them. The general consensus is that taking care of these patients is a dirty job … why do I have to do it?That's where I come in. It's a dirty job … and that's exactly why I do it. I run a unique service, where my preferred patients are those admitted for 6–8 weeks of IV antibiotics to treat their endocarditis. Some of these patients survive after discharge, but most don't. I know this. But it's my job to help them anyway. It just turns out that in these cases, help doesn't always look the way you think it will.In a perfect world, having a life-threatening infection would be the rock bottom these young people need to embrace a new way of life. Unfortunately, this world is far from perfect. Just as having diabetes doesn't make you stop wanting junk food, having endocarditis does not make you stop wanting drugs. In fact, it can be the opposite. [End Page 26] Drugs are often the coping tool these patients turn to. Happy? Use drugs. Sad? Use drugs. Scared? Use drugs. That's why it's hard. Addiction defies logic; it can be cunning, baffling, and powerful. Until you understand addiction, you'll never really find a way to treat these patients, let alone a way to enjoy treating them.We all have patients who change things for us. They shift our perspective, make us view our practice, our patients, and ourselves differently; patients who teach us the lessons not learned in school. I will never forget Jack, one of those "difficult patients." He taught me how to care for people who really can't be medically helped. It's a lesson that can take years to learn: You've got to let go of the outcome, and some solutions don't look the way you think they should. In this way, he helped me continue in this difficult work.I was a nearly new hospitalist, having just moved into this work from outpatient addiction care. Jack was a young man, 32 years old. He had presented to our hospital with endocarditis of the aortic and tricuspid valves secondary to IVDU. He was referred to my service when he was ineligible for valve replacement due to septic emboli in his brain and subsequent micro hemorrhage. The surgery team wanted him to recover from these events before considering surgical treatment.Jack was a big guy, over 6'2", with a weight to match. He was covered in tattoos—his back, arms, chest, and neck—not an inch was bare. His physical presence might be considered intimidating. Jack was a man of few words: he complained of very little, was often asleep during medical visits, never really left his room, and had no visitors. About four days after his arrival, nursing became concerned about illicit drug use. Despite the fact he had no orders for narcotics or other sedating meds, he was sleeping all the time. His drug screens were negative. Despite the lack of specific evidence, I was asked to take measures to ensure he was not using illicit drugs, which included placing him on a contract and ordering 1:1 observation.His fatigue was concerning, though not for drug use. A repeat ECHO showed that his aortic insufficiency was worsening. His tricuspid insufficiency was very bad from the start. His belly began to swell, followed by his... (shrink)

Epidemiological studies of chronic diseases began around the mid-20th century. Contrary to the infectious disease epidemiology which had prevailed at the beginning of the 20th century and which had focused on single agents causing individual diseases, the chronic disease epidemiology which emerged at the end of Word War II was a much more complex enterprise that investigated a multiplicity of risk factors for each disease. Involved in the development of chronic disease epidemi-ology were therefore fundamental discussions on the notion (...) of causality, especially the question when causal inferences could be justified. In this paper, I shall analyze the implicit normativity of these de-bates. First, I shall give a brief overview of the historical background on which chronic disease epi-demiology emerged and describe how the pioneer studies on smoking and lung cancer became icon of the major challenge that the emerging chronic disease epidemiology was facing: the impossibility of proving that statistical associations reflected causal relations. Next, I shall describe how the develop-ment from the monocausal enterprise of infectious disease epidemiology to the multicausal enterprise of chronic disease epidemiology gave rise to intense discussions of the possible criteria by which to establish causal relationships between a given factor and a particular disease. I shall show how the necessary and sufficient conditions expressed in the so-called Henle-Koch criteria that had proved useful for the 19th century investigations of infectious diseases remained an ideal, although clearly an unobtainable one. Thus, I shall show how 20th century chronic disease epidemiologists on the one hand were searching for a new set of general principles which would provide a logical framework for their investigations, but on the other hand admitted that they would have to accept something more "pragmatic". I shall analyze the various positions in this debate, arguing that the implacability of the debate was due to unrecognized normative issues. I shall argue that many insisted on a distinction between science and application that was untenable, but that due to this distinction the values in-volved in deciding whether or not to act on the basis of a hypothesis were rarely explicitly discussed and the decision therefore continued to appear as a matter of taste rather than the result of a cogent normative analysis. (shrink)

The “One Health” initiative promises to combine different health-related issues concerning humans and animals in an overarching concept and in related practices to the benefit of both humans and animals. Far from dismissing One Health, this paper nevertheless argues that different veterinary interventions are determined by social practices and connected expectations and are, thus, hardly compliant with only one single conceptualization of health, as the One Health concept suggests. One Health relies on a naturalistic understanding of health focusing on similar (...) bodies that show a similar etiology. However, logics, normativity, and practices exhibit differences when it comes to combatting infectious diseases, maintaining productivity of livestock animals or preventing companion animals from suffering. Therefore, drawing from Charles Rosenberg’s groundbreaking texts on framing disease, we suggest to conceive of health as dispersed in different frames. Thus, this paper proposes to interpret health as complex and multi-layered concept. We distinguish and introduce an objectivist, a functional, and a sentientistic frame of health. Instead of reducing the differential veterinary practices to one paradigmatic understanding, health is seen as a model case of Wittgenstein’s concept of family resemblance. Different and distinct perspectives on veterinary medicine show sufficient overlapping that allows for a common conceptualization, but there is not one single underlying logic suitable to understand and ethically reflect all veterinary interventions. This differentiability promises to reduce moral stress in veterinary professionals since it allows the interpretation of various, seemingly contradicting practices as dependent on multi-layered and socially determined scopes of responsibility. (shrink)

Dispositions and tendencies feature significantly in the biomedical domain and therefore in representations of knowledge of that domain. They are not only important for specific applications like an infectious disease ontology, but also as part of a general strategy for modelling knowledge about molecular interactions. But the task of representing dispositions in some formal ontological systems is fraught with several problems, which are partly due to the fact that Description Logics can only deal well with binary relations. The (...) paper will discuss some of the results of the philosophical debate about dispositions, in order to see whether the formal relations needed to represent dispositions can be broken down to binary relations. Finally, we will discuss problems arising from the possibility of the absence of realizations, of multi-track or multi-trigger dispositions and offer suggestions on how to deal with them. (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)

The empirical evidence often justifies belief in scientific theories. For instance, the great wealth of chemical and other relevant data leaves us with no real alternative to believing that matter is made of atoms. Similarly, the natural history of past and present organisms makes it irrational to deny that life on earth has evolved from a common ancestry. Again, the character and epidemiology of infectious diseases effectively establishes that they are caused by microbes. Peter Lipton did much to illuminate (...) the logic of these and many similar inferences. Often the observed facts admit of only one good theoretical explanation. Rationality therefore dictates that we infer the truth of this explanation. (shrink)

This article analyses the biochemical object of tnf inhibitors from the perspective of living with an autoimmune disease. The author tries to tease out how the concept of immune inhibition is used in tandem with the biochemical object of tnf inhibitors to dominate in defining and narrating what health and disease, normal and pathological, cure and healing can mean in the context of autoimmune bodies. Specifically, and within the ‘pathological’ framework of autoimmune diseases, the pharmacological treatment of tnf inhibition is (...) designed to suppress the ‘overly’ active immune system, thus acting as a negative or suppressing biochemical agent aimed at putting the ‘malfunctioning’ immune system back in balance. As can be seen in the current conjuncture, tnf inhibitors officially —and governmentally— place those taking them in a risk group, as they 'lower' their overall bodily immunity and make them more vulnerable to infectious diseases, while stabilizing their patho-logical, ‘over’-immune uninhibited condition. Part personal narrative of being diagnosed with an autoimmune condition, part speculative autoimmune theory inspired by such a diagnosis, the article ultimately calls for a different form of embodiment that is neither negative nor affirmative, and yet is resistant even to itself. (shrink)

This paper examines the debate over the human immunodeficiency virus (HIV) as the cause of acquired immunodeficiency syndrome (AIDS) from an historical perspective. The changing criteria for proving the link between putative pathological agents and diseases are discussed, beginning with Robert Koch's research on anthrax in the late nineteenth century. Various versions of 'Koch's postulates' are analyzed in relation to the necessity and sufficiency arguments of logical reasoning. In addition, alterations to Koch's postulates are delineated, specifically those required by the (...) discovery of rickettsiae and viruses in the early twentieth century and by the immunological testing developed after midcentury to demonstrate the links between elusive viral agents and two diseases, hepatitis B and infectious mononucleosis. From this perspective, an examination of the AIDS debate is constructed. Molecular biologist Peter Duesberg's argument that HIV is not the cause of AIDS is analyzed in light of his contention that a version of Koch's postulates has not been satisfied. Additional research findings through 1990 relating to the etiology of AIDS are also noted. (shrink)

I read Stefan Collini’s What are Universities For? last week with very mixed feelings. In the past, I’ve much admired his polemical essays on the REF, “impact”, the Browne Report, etc. in the London Review of Books and elsewhere: they speak to my heart. If you don’t know those essays, you can get some of their flavour from his latest article in the Guardian yesterday. But I found the book a disappointment. Perhaps the trouble is that Collini is too decent, (...) too high-minded, has too unrealistically exalted a view about what actually happens in universities which is too coloured by attitudes appropriate to the traditional humanities. And he is optimistic to the point of fantasy if he thinks that people are so susceptible to “the romance of ideas and the power of beauty” that they will want, or can be brought to want, lots and lots of universities in order to promote the ideas (as if they would suppose that the task of “conserving, understanding, extending and handing on to subsequent generations the intellectual, scientific, and artistic heritage of mankind” was clearly ill-served when there were only forty universities in England, as opposed to a hundred and whatever). (shrink)

Multi-modal versions of propositional logics S5 or S4—commonly accepted as logics of knowledge—are capable of describing static states of knowledge but they do not reflect how the knowledge changes after communications among agents. In the present paper (part of broader research on logics of knowledge and communications) we define extensions of the logic S5 which can deal with public communications. The logics have natural semantics. We prove some completeness, decidability and interpretability results and formulate a general (...) method that solves certain kind of problems involving public communications—among them well known puzzles of Muddy Children and Mr. Sum & Mr. Product. As the paper gives a formal logical treatment of the operation of restriction of the universe of a Kripke model, it contributes also to investigations of semantics for modal logics. (shrink)

The aim of the present book is to give a comprehensive account of the ‘state of the art’ of substructural logics, focusing both on their proof theory and on their semantics (both algebraic and relational. It is for graduate students in either philosophy, mathematics, theoretical computer science or theoretical linguistics as well as specialists and researchers.

Retroduction -- Contextualized self-interpretations -- Causal mechanisms -- Ontology -- Logics -- Articulation.

This is a review of A. Skodo (ed.) "Other Logics: Alternatives to Formal Logic in the History of Thought and Contemporary Philosophy".

The First International Workshop brings together researchers from the theoretical ends of the logic programming and artificial intelligence communities to discuss their mutual interests. Logic programming deals with the use of models of mathematical logic as a way of programming computers, where theoretical AI deals with abstract issues in modeling and representing human knowledge and beliefs. One common ground is nonmonotonic reasoning, a family of logics that includes room for the kinds of variations that can be found in human (...) reasoning. Topics covered: Stable Semantics. Default Logic. AutoEpistemic Logic. Truth Maintenance Systems. Implementation Issues. Diagnosis. Applications. Inheritance Reasoning. Logics of Belief. Inconsistency and Non-Monotonicity. (shrink)

The Aristotelian syllogistic cannot account for the validity of certain inferences involving relational facts. In this paper, we investigate the prospects for providing a relational syllogistic. We identify several fragments based on (a) whether negation is permitted on all nouns, including those in the subject of a sentence; and (b) whether the subject noun phrase may contain a relative clause. The logics we present are extensions of the classical syllogistic, and we pay special attention to the question of whether (...) reductio ad absurdum is needed. Thus our main goal is to derive results on the existence (or nonexistence) of syllogistic proof systems for relational fragments. We also determine the computational complexity of all our fragments. (shrink)

In this paper, I will describe a technique for generating a novel kind of semantics for a logic, and explore some of its consequences. It would be natural to call the semantics produced by the technique in question ‘many-valued'; but that name is, of course, already taken. I call them, instead, ‘plurivalent'. In standard logical semantics, formulas take exactly one of a bunch of semantic values. I call such semantics ‘univalent'. In a plurivalent semantics, by contrast, formulas may take one (...) or more such values. The construction I shall describe can be applied to any univalent semantics to produce a corresponding plurivalent one. In the paper I will be concerned with the application of the technique to propositional many-valued logics. Sometimes going plurivalent does not change the consequence relation; sometimes it does. I investigate the possibilities in detail with respect to small family of many-valued logics. (shrink)

This chapter contains sections titled: 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9.

We study here extensions of the Artemov's logic of proofs in the language with quantifiers on proof variables. Since the provability operator □ A could be expressed in this language by the formula u[u]A, the corresponding logic naturally extends the well-known modal provability logic GL. Besides, the presence of quantifiers on proofs allows us to study some properties of provability not covered by the propositional logics.In this paper we study the arithmetical complexity of the provability logic with quantifiers on (...) proofs for a given arithmetical theory T and a class of proof predicates.In the last section we define Kripke style semantics for the logics corresponding to the standard Gödel proof predicate and its multiple conclusion version. (shrink)

This book constitutes the strictly refereed post-workshop proceedings of the 11th International Workshop on Computer Science Logic, CSL '97, held as the 1997 Annual Conference of the European Association on Computer Science Logic, EACSL, in Aarhus, Denmark, in August 1997. The volume presents 26 revised full papers selected after two rounds of refereeing from initially 92 submissions; also included are four invited papers. The book addresses all current aspects of computer science logics and its applications and thus presents the (...) state of the art in the area. (shrink)

We will present all the mixed and impure disjoint three-valued logics based on the Strong Kleene schema. Some, but not all of them, are (inferentially) empty logics. We will also provide a recipe to build philosophical interpretations for each of these logics, and show why the kind of permeability that characterized them is not such a bad feature.

This volume examines the concept of falsification as a central notion of semantic theories and its effects on logical laws. The point of departure is the general constructivist line of argument that Michael Dummett has offered over the last decades. From there, the author examines the ways in which falsifications can enter into a constructivist semantics, displays the full spectrum of options, and discusses the logical systems most suitable to each one of them. While the idea of introducing falsifications into (...) the semantic account is Dummett's own, the many ways in which falsificationism departs quite radically from verificationism are here spelled out in detail for the first time. The volume is divided into three large parts. The first part provides important background information about Dummett’s program, intuitionism and logics with gaps and gluts. The second part is devoted to the introduction of falsifications into the constructive account and shows that there is more than one way in which one can do this. The third part details the logical effects of these various moves. In the end, the book shows that the constructive path may branch in different directions: towards intuitionistic logic, dual intuitionistic logic and several variations of Nelson logics. The author argues that, on balance, the latter are the more promising routes to take. "Kapsner’s book is the first detailed investigation of how to incorporate the notion of falsification into formal logic. This is a fascinating logico-philosophical investigation, which will interest non-classical logicians of all stripes." Graham Priest, Graduate Center, City University of New York and University of Melbourne. (shrink)