We study a fragment of Intuitionistic Linear Logic combined with non-normal modal operators. Focusing on the minimal modal logic, we provide a Gentzen-style sequent calculus as well as a semantics in terms of Kripke resource models. We show that the proof theory is sound and complete with respect to the class of minimal Kripke resource models. We also show that the sequent calculus allows cut elimination. We put the logical framework to use by instantiating it as a logic (...) of agency. In particular, we apply it to reason about the resource-sensitive use of artefacts. (shrink)

The reductive, as opposed to deductive, view of logic is the form of logic that is, perhaps, most widely employed in practical reasoning. In particular, it is the basis of logic programming. Here, building on the idea of uniform proof in reductive logic, we give a treatment of logic programming for BI, the logic of bunched implications, giving both operational and denotational semantics, together with soundness and completeness theorems, all couched in terms of the resource interpretation of BI’s semantics. (...) We use this set-up as a basis for exploring how coalgebraic semantics can, in contrast to the basic denotational semantics, be used to describe the concrete operational choices that are an essential part of proof-search. The overall aim, toward which this paper can be seen as an initial step, is to develop a uniform, generic, mathematical framework for understanding the relationship between the deductive structure of logics and the control structures of the corresponding reductive paradigm. (shrink)

This paper presents statistical default logic, an expansion of classical (i.e., Reiter) default logic that allows us to model common inference patterns found in standard inferential statistics, including hypothesis testing and the estimation of a populations mean, variance and proportions. The logic replaces classical defaults with ordered pairs consisting of a Reiter default in the first coordinate and a real number within the unit interval in the second coordinate. This real number represents an upper-bound limit on the probability of accepting (...) the consequent of an applied default and that consequent being false. A method for constructing extensions is then defined that preserves this upper bound on the probability of error under a (skeptical) non-monotonic consequence relation. (shrink)

We introduce the logic LRC, designed to describe and reason about agents’ abilities and capabilities in using resources. The proposed framework bridges two—up to now—mutually independent strands of literature: the one on logics of abilities and capabilities, developed within the theory of agency, and the one on logics of resources, motivated by program semantics. The logic LRC is suitable to describe and reason about key aspects of social behaviour in organizations. We prove a number of properties enjoyed by (...) LRC and its associated analytic calculus. These results lay at the intersection of the algebraic theory of unified correspondence and the theory of multitype calculi in structural proof theory. Case studies are discussed which showcase several ways in which this framework can be extended and enriched while retaining its basic properties, so as to model an array of issues, both practically and theoretically relevant, spanning from planning problems to the logical foundations of the theory of organizations. (shrink)

The description of resources in game semantics has never achieved the simplicity and precision of linear logic, because of the misleading conception that linear logic is more primitive than game semantics. Here, we defend the opposite view, and thus advocate that game semantics is conceptually more primitive than linear logic. This revised point of view leads us to introduce tensor logic, a primitive variant of linear logic where negation is not involutive. After formulating its categorical semantics, we interpret tensor logic (...) in a model based on Conway games equipped with a notion of payoff, in order to reflect the various resource policies of the logic: linear, affine, relevant or exponential. (shrink)

Syntactic logics do not suffer from the problems of logical omniscience but are often thought to lack interesting properties relating to epistemic notions. By focusing on the case of rule-based agents, I develop a framework for modelling resource-bounded agents and show that the resulting models have a number of interesting properties.

We propose a framework for modelling situated resource-bounded agents. The framework is based on an objective ascription of intentional modalities and can be easily tailored to the system we want to model and the properties we wish to specify. As an elaboration of the framework, we introduce a logic, OBA, for describing the observations, beliefs, goals and actions of simple agents, and show that OBA is complete, decidable and has an efficient model checking procedure, allowing properties of agents specified (...) in OBA to be verified using standard theorem proving or model checking techniques. (shrink)

In this paper we continue the study of Girard's Linear Logic and introduce a new Linear Logic with modalities. Our logic describes not only the consumption, but also the presence of resources. We introduce a new semantics and a new calculus for this logic. In contrast to the results of Lincoln [7] and Kanovich [4] about the NP-completeness of the problem of the construction of a proof for a given sequent in the multiplicative fragment of Girard's Linear Logic, we present (...) here a non-exponential algorithm to construct a proof for a given sequent and a given point of a given model in our Linear Logic. (shrink)

This article focuses on medical trials performed by Dr. Albert Kligman on the inmates of Philadelphia's Holmesburg Prison between 1951 and 1974, which have been widely criticized as exploitative. I seek to investigate the mechanics behind the “ethical blind spot” that enabled the American medical community to laud Kligman for his efforts while simultaneously condemning the medical atrocities of the Holocaust and supporting the development of the Nuremberg Code. I argue that this nonrecognition hinges on a colonial logic by which (...) certain populations are produced as waste, both rhetorically and materially. Drawing on the incarcerated men’s accounts included in Allen Hornblum’s books on the subject, I trace the process by which human beings come to be reclassified as natural resources and their exploitation recast as industrious cultivation. (shrink)

In this paper we introduce a new type of nets with bounded types of distributed resources . Linear Logic to describe the behaviour of BR-nets is defined. It is based on Girard's Linear Logic but captures not only consumption of resources but their presence as well. Theorem of soundness and completeness of the proposed axiomatization is proved and the complexity of the provability problem is established for the general case and some particular ones.

We propose a separation logic where resources are histories (sequences) of epistemic actions so that resource update means concatenation of histories and resource decomposition means splitting of histories. This separation logic, called AMHSL, allows us to reason about the past: does what is true now depend on what was true in the past, before certain actions were executed? We show that the multiplicative connectives can be eliminated from a logical language with also epistemic and action model modalities, if (...) the horizon of epistemic actions is bounded. (shrink)

A first-order temporal non-commutative logic TN[l], which has no structural rules and has some l-bounded linear-time temporal operators, is introduced as a Gentzen-type sequent calculus. The logic TN[l] allows us to provide not only time-dependent, resource-sensitive, ordered, but also hierarchical reasoning. Decidability, cut-elimination and completeness (w.r.t. phase semantics) theorems are shown for TN[l]. An advantage of TN[l] is its decidability, because the standard first-order linear-time temporal logic is undecidable. A correspondence theorem between TN[l] and a resource indexed non-commutative (...) logic RN[l] is also shown. This theorem is intended to state that “time” is regarded as a “resource”. (shrink)

Classical propositional logic plays a prominent role in industrial applications, and yet the complexity of this logic is presumed to be non-feasible. Tractable systems such as depth-bounded boolean logics approximate classical logic and can be seen as a model for resource-bounded agents whose reasoning style is nonetheless classical. In this paper we first study a hierarchy of tractable logics that is not defined by depth. Then we extend it into a modal logic where modalities make explicit the (...) assumptions discharged in propositional proofs, thereby expressing blueprints for proofs. A natural deduction system is provided that permits to reason about and manage such proof blueprints. (shrink)

Public or stakeholder participation in environmental governance has been strongly advocated within the United Nations (UN) since the early 1990s. A relatively new mechanism for global climate finance that emphasises stakeholder engagement is the Green Climate Fund (GCF), a UN strategy for channelling funds from the Global North to the Global South. Drawing on previous critical approaches to multi-stakeholder involvement in global governance, this article explores stakeholder involvement within the GCF. The study combines ideas from institutional logics and (...) class='Hi'>resource dependency to provide a better understanding of how stakeholder arrangements are shaped in climate organisations. Results show that the GCF stakeholder arrangement favours private sector stakeholders – stakeholders that take a technical and apolitical approach to climate finance – and disfavours smaller, less resourceful stakeholders as well as those who perform a politicised watchdog function. (shrink)

Does syllogistic logic have the resources to capture mathematical proof? This volume provides the first unified account of the history of attempts to answer this question, the reasoning behind the different positions taken, and their far-reaching implications. Aristotle had claimed that scientific knowledge, which includes mathematics, is provided by syllogisms of a special sort: 'scientific' ('demonstrative') syllogisms. In ancient Greece and in the Middle Ages, the claim that Euclid's theorems could be recast syllogistically was accepted without further scrutiny. Nevertheless, as (...) early as Galen, the importance of relational reasoning for mathematics had already been recognized. Further critical voices emerged in the Renaissance and the question of whether mathematical proofs could be recast syllogistically attracted more sustained attention over the following three centuries. Supported by more detailed analyses of Euclidean theorems, this led to attempts to extend logical theory to include relational reasoning, and to arguments purporting to reduce relational reasoning to a syllogistic form. Philosophical proposals to the effect that mathematical reasoning is heterogenous with respect to logical proofs were famously defended by Kant, and the implications of the debate about the adequacy of syllogistic logic for mathematics are at the very core of Kant's account of synthetic a priori judgments. While it is now widely accepted that syllogistic logic is not sufficient to account for the logic of mathematical proof, the history and the analysis of this debate, running from Aristotle to de Morgan and beyond, is a fascinating and crucial insight into the relationship between philosophy and mathematics. (shrink)

Tens of thousands of students have learned to be more discerning at constructing and evaluating arguments with the help of Patrick J. Hurley. Hurley’s lucid, friendly, yet thorough presentation has made A CONCISE INTRODUCTION TO LOGIC the most widely used logic text in North America. In addition, the book’s accompanying technological resources, such as CengageNOW and Learning Logic, include interactive exercises as well as video and audio clips to reinforce what you read in the book and hear in class. In (...) short, you’ll have all the assistance you need to become a more logical thinker and communicator. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version. (shrink)

Conceptualizing the nature of reality and the way the world functions, Ekaterina Yahyaoui Krivenko analyzes the foundations of human rights law in the strict subject/object dichotomy. Seeking to dismantle this dichotomy using topo-logic, a concept developed by Japanese philosopher Nishida Kitaro, this topical book formulates ways to operationalize alternative visions of human rights practice. Subject/object dichotomy, Yahyaoui Krivenko demonstrates, emerges from and reflects a particular Western worldview through a quest for rationality and formal logic. Taking a metaphysical and epistemological perspective, (...) this book explores the alternative views of reality and logic, developed by Kitaro, to demonstrate how topo-logic can enable both a theoretical and a practical renewal of human rights and overcome the subject/object dichotomy. Examining the recent growth of social movements, decolonization and diversification of discourses about human rights, and substantive equality, the book identifies these developments in contemporary human rights as indications of a movement towards a topo-logical view beyond the subject/object dichotomy. Students and scholars of critical legal studies, legal theory and philosophy, and international human rights law will find this book to be an invigorating read. Laying ground for the possible renewal and enhancement of human rights law, it will also be a useful resource for practitioners of human rights law. (shrink)

There are several areas in applied logic where deletion from databases is involved in one way or another:Belief contraction Triggers of the form ‘If condition then remove A’, which are extensively used in database management systemsResource considerations as in relevance and linear logics, where addition or removal of resource can affect provabilityFree logic and the like, where existence and non-existence of individuals affects quantification.All of these areas have certain logical difficulties relating to the removal of elements. These difficulties (...) are normally overcome by working on the meta-level. This paper offers a comprehensive model in which the various forms of removal are treated on the object level, i.e., as connectives of the object language. (shrink)

There are several areas in applied logic where deletion from databases is involved in one way or another:Belief contraction Triggers of the form ‘If condition then remove A’, which are extensively used in database management systemsResource considerations as in relevance and linear logics, where addition or removal of resource can affect provabilityFree logic and the like, where existence and non-existence of individuals affects quantification.All of these areas have certain logical difficulties relating to the removal of elements. This paper (...) points out the difficulties and offers a comprehensive logical model. (shrink)

Formal nonmonotonic systems try to model the phenomenon that common sense reasoners are able to “jump” in their reasoning from assumptions Δ to conclusions C without their being any deductive chain from Δ to C. Such jumps are done by various mechanisms which are strongly dependent on context and knowledge of how the actual world functions. Our aim is to motivate these jump rules as inference rules designed to optimise survival in an environment with scant resources of effort and time. (...) We begin with a general discussion and quickly move to Section 3 where we introduce five resource principles. We show that these principles lead to some well known nonmonotonic systems such as Nute’s defeasible logic. We also give several examples of practical reasoning situations to illustrate our principles. (shrink)

The logical omniscience problem, whereby standard models of epistemic logic treat an agent as believing all consequences of its beliefs and knowing whatever follows from what else it knows, has received plenty of attention in the literature. But many attempted solutions focus on a fairly narrow specification of the problem: avoiding the closure of belief or knowledge, rather than showing how the proposed logic is of philosophical interest or of use in computer science or artificial intelligence. Sentential epistemic logics, (...) as opposed to traditional possible worlds approaches, do not suffer from the problems of logical omniscience but are often thought to lack interesting epistemic properties. In this paper, I focus on the case of rule-based agents, which play a key role in contemporary AI research but have been neglected in the logical literature. I develop a framework for modelling monotonic, nonmonotonic and introspective rule-based reasoners which have limited cognitive resources and prove that the resulting models have a number of interesting properties. An axiomatization of the resulting logic is given, together with completeness, decidability and complexity results. (shrink)

An agent-centered, goal-directed, resource-bound logic of human reasoning would do well to note that individual cognitive agency is typified by the comparative scantness of available cognitive resources—information, time, and computational capacity, to name just three. This motivates individual agents to set their cognitive agendas proportionately, that is, in ways that carry some prospect of success with the resources on which they are able to draw. It also puts a premium on cognitive strategies which make economical use of those resources. (...) These latter I callscant-resource adjustment strategies,and they supply the context for an analysis of abduction. The analysis is Peircian in tone, especially in the emphasis it places on abduction’signorance-preservingcharacter. My principal purpose here is to tie abduction’s scarce-resource adjustment capacity to its ignorance preservation. (shrink)

Timothy Williamson gives an original and provocative treatment of deep metaphysical questions about existence, contingency, and change, using the latest resources of quantified modal logic. Contrary to the widespread assumption that logic and metaphysics are disjoint, he argues that modal logic provides a structural core for metaphysics.

Supported by a qualitative study of triple bottom line firms—those that simultaneously prioritize economic, social, and environmental objectives—we investigated the market logic and practices of TBL firms to better understand how they fulfill their mission and achieve their goals. We explored if and how TBL firms may differ in their approach to stakeholders and the management of their resources, including dynamic capabilities. We employed a research design that emphasizes the iterative comparison of narrative data within themselves and with scholarly literature (...) [i.e., resource-based view ] to develop new theoretical insights. Because the RBV is commonly used to theorize how firms achieve competitive advantage, we explored whether TBL firms achieve competitive advantage differently from what RBV theory would predict. Our data suggest that how a firm defines value has a significant influence on the capabilities it creates and how it treats its resources. We find that TBL firms redefine value to not only focus on the end product or service but also to include the systemic cost of delivering goods. As a result, TBL firms differ from prevailing scholarly thought in RBV. They strive to have resources that are sustainable and therefore imitable, commonly found, and substitutable. Moreover, they are not only transparent in their processes but also collaborate with others in the value chain and in their sector. In doing so, they deliberately create new markets from which other firms can benefit. Rather than focusing on competitive advantage, they focus on collaborative advantage. (shrink)

The traditional possible-worlds model of belief describes agents as ‘logically omniscient’ in the sense that they believe all logical consequences of what they believe, including all logical truths. This is widely considered a problem if we want to reason about the epistemic lives of non-ideal agents who—much like ordinary human beings—are logically competent, but not logically omniscient. A popular strategy for avoiding logical omniscience centers around the use of impossible worlds: worlds that, in one way or another, violate the laws (...) of logic. In this paper, we argue that existing impossible-worlds models of belief fail to describe agents who are both logically non-omniscient and logically competent. To model such agents, we argue, we need to ‘dynamize’ the impossible-worlds framework in a way that allows us to capture not only what agents believe, but also what they are able to infer from what they believe. In light of this diagnosis, we go on to develop the formal details of a dynamic impossible-worlds framework, and show that it successfully models agents who are both logically non-omniscient and logically competent. (shrink)

This article examines the potential for moral agency in human resource management practice. It draws on an ethnographic study of human resource managers in a global organization to provide a theorized account of situated moral agency. This account suggests that within contemporary organizations, institutional structures—particularly the structures of Anglo-American market capitalism— threaten and constrain the capacity of HR managers to exercise moral agency and hence engage in ethical behaviour. The contextualized explanation of HR management action directly addresses the (...) question of whether HRM is inherently unethical. The discussion draws on MacIntyre’s conceptualization of moral agency within contemporary social structures. In practice, HR managers embody roles that may not be wholly compartmentalized. Alternative institutional structures can provide HR managers with a vocabulary of motives for people-centred HRM and widen the scope for the exercising of moral agency, when enacted within reflective relational spaces that provide milieus for critical questioning of logics and values. This article aims to contribute to and extend debate on whether HRM can ever be ethical, and provide a means of reconnecting business ethics with longstanding concerns in critical management studies. (shrink)

The paper highlights proof-theoretic semantics as providing natural resources for capturing semantic variation in natural language. The semantic variations include:Distinction between extensional predication and attribution to intensional transitive verbs a non-specific object.Omission of a verbal argument in a transitive verb.Obtaining sameness of meaning of sentences with transitive verbs with omitted object and existentially quantified object.Blocking unwarranted entailments in adjective–noun combinations.Capturing quantifier scope ambiguity.Obtaining context dependent quantifier domain restriction. The proof-theoretic resources employed to capture the above semantic variations include:The use of (...) different kinds of formal parameters and different ways of binding them to predicates.Omission of a premise from a proof-rule.Basing meanings on derivations in meaning-conferring proof-systems.Appealing to substructurality of I/E-rules.Controlling the order of rule applications in derivations.Controlling the open formulas participating in a context within a sequent. (shrink)

The AGM paradigm for belief revision provides a very elegant and powerful framework for reasoning about idealized agents. The paradigm assumes that the modeled agent is a perfect reasoner with infinite memory. In this paper we propose a framework to reason about non-ideal agents that generalizes the AGM paradigm. We first introduce a structure to represent an agent's belief states that distinguishes different status of beliefs according to whether or not they are explicitly represented, whether they are currently active and (...) whether they are fully accepted or provisional. Then we define a set of basic operations that change the status of beliefs and show how these operations can be used to model agents with different capacities. We also show how different operations of belief change described in the literature can be seen as special cases of our theory. (shrink)

In this overview article, we first explain what we take informal logic to be, discussing misconceptions and distinguishing our conception of it from competing ones; second, we briefly catalogue recent informal logic research, under 14 headings; third, we suggest four broad areas of problems and questions for future research; fourth, we describe current scholarly resources for informal logic; fifth, we discuss three implications of informal logic for philosophy in particular, and take note ofpractical consequences of a more general sort.

We explore the view that Frege's puzzle is a source of straightforward counterexamples to Leibniz's law. Taking this seriously requires us to revise the classical logic of quantifiers and identity; we work out the options, in the context of higher-order logic. The logics we arrive at provide the resources for a straightforward semantics of attitude reports that is consistent with the Millian thesis that the meaning of a name is just the thing it stands for. We provide models to (...) show that some of these logics are non-degenerate. (shrink)

This book investigates the central role of reason in Islamic intellectual life. Despite widespread characterization of Islam as a system of belief based only on revelation, John Walbridge argues that rational methods, not fundamentalism, have characterized Islamic law, philosophy and education since the medieval period. His research demonstrates that this medieval Islamic rational tradition was opposed by both modernists and fundamentalists, resulting in a general collapse of traditional Islamic intellectual life and its replacement by more modern but far shallower forms (...) of thought. However, the resources of this Islamic scholarly tradition remain an integral part of the Islamic intellectual tradition and will prove vital to its revival. The future of Islam, Walbridge argues, will be marked by a return to rationalism"--Provided by publisher. (shrink)

Work on analogy has been done from a number of disciplinary perspectives throughout the history of Western thought. This work is a multidisciplinary guide to theorizing about analogy. It contains 1,406 references, primarily to journal articles and monographs, and primarily to English language material. classical through to contemporary sources are included. The work is classified into eight different sections (with a number of subsections). A brief introduction to each section is provided. Keywords and key expressions of importance to research on (...) analogy are discussed in the introductory material. Electronic resources for conducting research on analogy are listed as well. (shrink)

This book addresses the logical aspects of the foundations of scientific theories. Even though the relevance of formal methods in the study of scientific theories is now widely recognized and regaining prominence, the issues covered here are still not generally discussed in philosophy of science. The authors focus mainly on the role played by the underlying formal apparatuses employed in the construction of the models of scientific theories, relating the discussion with the so-called semantic approach to scientific theories. The book (...) describes the role played by this metamathematical framework in three main aspects: considerations of formal languages employed to axiomatize scientific theories, the role of the axiomatic method itself, and the way set-theoretical structures, which play the role of the models of theories, are developed. The authors also discuss the differences and philosophical relevance of the two basic ways of aximoatizing a scientific theory, namely Patrick Suppes’ set theoretical predicates and the "da Costa and Chuaqui" approach. This book engages with important discussions of the nature of scientific theories and will be a useful resource for researchers and upper-level students working in philosophy of science. (shrink)

Natural language does not express all connectives definable in classical logic as simple lexical items. Coordination in English is expressed by conjunction and, disjunction or, and negated disjunction nor. Other languages pattern similarly. Non-lexicalized connectives are typically expressed compositionally: in English, negated conjunction is typically expressed by combining negation and conjunction (not both). This is surprising: if $$\wedge $$ ∧ and $$\vee $$ ∨ are duals, and the negation of the latter can be expressed lexically (nor), why not the negation (...) of the former? I present a two-tiered model of the semantics of the binary connectives. The first tier captures the expressive power of the lexicon: it is a bilateral state-based semantics that, under a restriction, can express all and only the distinctions that can be expressed by the lexicon of natural language (and, or, nor). This first tier is characterized by rejection as non-assertion and a Neglect Zero assumption. The second tier is obtained by dropping the Neglect Zero assumption and enforcing a stronger notion of rejection, thereby recovering classical logic and thus definitions for all Boolean connectives. On the two-tiered model, we distinguish the limited expressive resources of the lexicon and the greater combinatorial expressive power of the language as a whole. This gives us a logic-based account of compositionality for the Boolean fragment of the language. (shrink)

In the Newcomb problem, the standard arguments for taking either one box or both boxes adduce what seem to be relevant considerations, but they are not complete arguments, and attempts to complete the arguments rely upon incorrect principles of rational decision making. It is argued that by considering how the predictor is making his prediction, we can generate a more complete argument, and this in turn supports a form of causal decision theory.

This paper investigates whether the fundamental linguistic insights and intuitions of Lexical Functional Grammar, which is usually presented as a constraint-based linguistic theory, can be reformulated in a resource sensitive framework using a substructural modal logic. In the approach investigated here, LFG's f-descriptions are replaced with expressions from a multi-modal propositional logic. In effect, the feature structure unification basis of LFG's f-structures is replaced with a very different resource based mechanism. It turns out that some linguistic analyses that (...) required non-monotonic devices in LFG analysis of Icelandic) can be straightforwardly expressed in the framework presented here. Moreover, a Curry– Howard correspondence between proofs in this logic and -terms provides a semantic interpretation as a by-product of the process of showing syntactic well-formedness. (shrink)

This monograph explores the logical systems of early logicians in the Arabic tradition from a theoretical perspective, providing a complete panorama of early Arabic logic and centering it within an expansive historical context. By thoroughly examining the writings of the first Arabic logicians, al-Fārābī, Avicenna and Averroes, the author analyzes their respective theories, discusses their relationship to the syllogistics of Aristotle and his followers, and measures their influence on later logical systems. Beginning with an introduction to the writings of the (...) most prominent Arabic logicians, the author scrutinizes these works to determine their categorical logic, as well as their modal and hypothetical logics. Where most other studies written on this subject focus on the Arabic logicians’ epistemology, metaphysics, and theology, this volume takes a unique approach by focusing on the actual technical aspects and features of their logics. The author then moves on to examine the original texts as closely as possible and employs the symbolism of modern propositional, predicate, and modal logics, rendering the arguments of each logician clearly and precisely while clarifying the theories themselves in order to determine the differences between the Arabic logicians’ systems and those of Aristotle. By providing a detailed examination of theories that are still not very well-known in Western countries, the author is able to assess the improvements that can be found in the Arabic writings, and to situate Arabic logic within the breadth of the history of logic. This unique study will appeal mainly to historians of logic, logicians, and philosophers who seek a better understanding of the Arabic tradition. It also will be of interest to modern logicians who wish to delve into the historical aspects and progression of their discipline. Furthermore, this book will serve as a valuable resource for graduate students who wish to complement their general knowledge of Arabic culture, logic, and sciences. (shrink)

Agents need to be able to change their beliefs; in particular, they should be able to contract or remove a certain belief in order to restore consistency to their set of beliefs, and revise their beliefs by incorporating a new belief which may be inconsistent with their previous beliefs. An influential theory of belief change proposed by Alchourron, G¨ardenfors and Makinson (AGM) [1] describes postulates which a rational belief revision and contraction operations should satisfy. The AGM postulates have been perceived (...) as characterising idealised rational reasoners, and the corresponding belief change operations are considered unsuitable for implementable agents due to their high computational cost [3]. The main result of this paper is showing that an efficient (linear time) belief contraction operation nevertheless satisfies all but one of the AGM postulates for contraction. This contraction operation is defined for a realistic rule-based agent which can be seen as a reasoner in a very weak logic; although the agent’s beliefs are deductively closed with respect to this logic, checking consistency and tracing dependencies between beliefs is not computationally expensive. Finally, we give a non-standard definition of belief revision in terms of contraction for our agent. (shrink)

The chapters in this timely volume aim to answer the growing interest in Arthur Schopenhauer’s logic, mathematics, and philosophy of language by comprehensively exploring his work on mathematical evidence, logic diagrams, and problems of semantics. Thus, this work addresses the lack of research on these subjects in the context of Schopenhauer’s oeuvre by exposing their links to modern research areas, such as the “proof without words” movement, analytic philosophy and diagrammatic reasoning, demonstrating its continued relevance to current discourse on logic. (...) -/- Beginning with Schopenhauer’s philosophy of language, the chapters examine the individual aspects of his semantics, semiotics, translation theory, language criticism, and communication theory. Additionally, Schopenhauer’s anticipation of modern contextualism is analyzed. The second section then addresses his logic, examining proof theory, metalogic, system of natural deduction, conversion theory, logical geometry, and the history of logic. Special focus is given to the role of the Euler diagrams used frequently in his lectures and their significance to broader context of his logic. In the final section, chapters discuss Schopenhauer’s philosophy of mathematics while synthesizing all topics from the previous sections, emphasizing the relationship between intuition and concept. -/- Aimed at a variety of academics, including researchers of Schopenhauer, philosophers, historians, logicians, mathematicians, and linguists, this title serves as a unique and vital resource for those interested in expanding their knowledge of Schopenhauer’s work as it relates to modern mathematical and logical study. (shrink)

Justification logics are a family of modal logics whose non-normal modalities are parametrised by a type-theoretic calculus of terms. The first justification logic was developed by Sergei Artemov to provide an explicit modal logic for arithmetical provability in which these terms were taken to pick out proofs. But, justification logics have been given various other interpretations as well. In this paper, we will rely on an interpretation in which the modality \ is read ‘S accepts \ as (...) justification for \’. Since it is often important to specify just how much confidence agents have in propositions on the basis of justifications, the logic will need to be extended if it is to provide a sufficiently general account. The primary purpose of this paper is to extend justification logic with the expressive resources to needed to do so. Thus, we will construct the justification logic with confidence ). While \ will be extremely general, capable of accommodating a wide range of interpretations, we provide motivation in terms of the notion of confidence deriving recent work by Paul and Quiggin :363–382, 2018). Under this understanding, confidence must only correspond to a partial ordering. We axiomatise \ and provide a sound and complete semantics. (shrink)

What does it mean for the laws of logic to fail? My task in this paper is to answer this question. I use the resources that Routley/Sylvan developed with his collaborators for the semantics of relevant logics to explain a world where the laws of logic fail. I claim that the non-normal worlds that Routley/Sylvan introduced are exactly such worlds. To disambiguate different kinds of impossible worlds, I call such worlds logically impossible worlds. At a logically impossible world, the (...) laws of logic fail. In this paper, I provide a definition of logically impossible worlds. I then show that there is nothing strange about admitting such worlds. (shrink)

This is a wide-ranging 2004 book about arguments for and against beliefs in God. The arguments for the belief are analysed in the first six chapters and include ontological arguments from Anselm to Gödel, the cosmological arguments of Aquinas and Leibniz, and arguments from evidence for design and miracles. The next two chapters consider arguments against belief. The last chapter examines Pascalian arguments for and against belief in God. There are discussions of Cantorian problems for omniscience, of challenges to divine (...) omnipotence, and of the compatibility of everlasting complete knowledge of the world with free-will. There are appendices that present formal proofs in a system for quantified modal logic, a theory of possible worlds, notes on Cantorian set theory, and remarks concerning non-standard hyperreal numbers. This book will be a valuable resource for philosophers of religion and theologians and will interest logicians and mathematicians as well. (shrink)

I criticize conceptual pluralism, as endorsed recently by John Dupre and Philip Kitcher, for failing to supply strategies for demarcating science from non-science. Using creation-science as a test case, I argue that pluralism blocks arguments that keep creation-science in check and that metaphysical pluralism offers it positive, metaphysical support. Logical empiricism, however, still provides useful resources to reconfigure and manage the problem of creation-science in those practical and political contexts where pluralism will fail.