Many problems in Multi-Agent Systems (MASs) research are formulated in terms of the abilities of a coalition of agents. Existing approaches to reasoning about coalitional ability are usually focused on games or transition systems, which are described in terms of states and actions. Such approaches however often neglect a key feature of multi-agent systems, namely that the actions of the agents require resources. In this paper, we describe a logic for reasoning about coalitional ability under resource constraints in the probabilistic (...) setting. We extend Resource-bounded Alternating-time Temporal Logic (RB-ATL) with probabilistic reasoning and provide a standard algorithm for the model-checking problem of the resulting logic Probabilistic resource-bounded ATL (pRB-ATL). We implement model-checking algorithms and present experimental results using simple multi-agent model-checking problems of increasing complexity. (shrink)

Modelling with Words is an emerging modelling methodology closely related to the paradigm of Computing with Words introduced by Lotfi Zadeh. This book is an authoritative collection of key contributions to the new concept of Modelling with Words. A wide range of issues in systems modelling and analysis is presented, extending from conceptual graphs and fuzzy quantifiers to humanist computing and self-organizing maps. Among the core issues investigated are - balancing predictive accuracy and high level transparency in learning - scaling (...) linguistic algorithms to high-dimensional data problems - integrating linguistic expert knowledge with knowledge derived from data - identifying sound and useful inference rules - integrating fuzzy and probabilistic uncertainty in data modelling. (shrink)

I argue that normative formal epistemology (NFE) is best understood as modelling, in the sense that this is the reconstruction of its methodology on which NFE is doing best. I focus on Bayesianism and show that it has the characteristics of modelling. But modelling is a scientific enterprise, while NFE is normative. I thus develop an account of normative models on which they are idealised representations put to normative purposes. Normative assumptions, such as the transitivity of comparative credence, are (...) characterised as modelling idealisations motivated normatively. I then survey the landscape of methodological options: what might formal epistemologists be up to? I argue the choice is essentially binary: modelling or theorising. If NFE is theorising it is doing very poorly: generating false claims with no clear methodology for separating out what is to be taken seriously. Modelling, by contrast, is a successful methodology precisely suited to the management of useful falsehoods. Regarding NFE as modelling is not costless, however. First, our normative inferences are less direct and are muddied by the presence of descriptive idealisations. Second, our models are purpose-specific and limited in their scope. I close with suggestions for how to adapt our practice. (shrink)

A formal neuron has been studied mathematically. The spiking behaviour of a single neuron has been considered and the influence of the other neurons has been replaced by an average activity level. Four different kinds of spiking behaviour are predicted by the model: B (bursts), C (continuous), P (periodic) and S (silent) neurons and several real neurons can be classified within these four categories. Some properties of the spiking neuron are calculated: 1) the time between spikes, 2) the spike (...) train length and 3) the silent time. Because these magnitudes can be measured in the laboratory, an experimental validation of the model is proposed. (shrink)

Special issue. With contributions by Rogier De Langhe and Matthias Greiff, Igor Douven and Alexander Riegler, Stephan Hartmann and Jan Sprenger, Carl Wagner, Paul Weirich, and Jesús Zamora Bonilla.

One approach to applied AI is to automate business processes and remove people from the system. Another approach is to use AI methods to model how work actually gets done, so we can understand the essential role of knowledge people have about each other ("social knowledge") in allocating resources, assigning jobs, and forming teams.

The origins of human social cooperation confound simple evolutionary explanation. But from Darwin and Durkheim onward, theorists (anthropologists and sociologists especially) have posited a potential link with another curious and distinctively human social trait that cries out for explanation: religion. This dissertation explores one contemporary theory of the co-evolution of religion and human social cooperation: the signalling theory of religion, or religious signalling theory (RST). According to the signalling theory, participation in social religion (and its associated rituals and sanctions) acts (...) as an honest signal of one’s commitment to a religiously demarcated community and its way of doing things. This signal would allow prosocial individuals to positively assort with one another for mutual advantage, to the exclusion of more exploitative individuals. In effect, the theory offers a way that religion and cooperation might explain one another, but which that stays within an individualist adaptive paradigm. My approach is not to assess the empirical adequacy of the religious signalling explanation or contrast it with other explanations, but rather to deal with the theory in its own terms – isolating and fleshing out its core commitments, explanatory potential, and limitations. The key to this is acknowledging the internal complexities of signalling theory, with respect to the available models of honest signalling and the extent of their fit (or otherwise) with religion as a target system. The method is to take seriously the findings of formal modelling in animal signalling and other disciplines, and to apply these (and methods from the philosophy of biology more generally) to progressively build up a comprehensive picture of the theory, its inherent strengths and weaknesses. The first two chapters outline the dual explanatory problems that cooperation and religion present for evolutionary human science, and surveys contemporary approaches toward explaining them. Chapter three articulates an evolutionary conception of the signalling theory, and chapters four to six make the case for a series of requirements, limitations, and principles of application. Chapters seven and eight argue for the value of formal modelling to further flesh out the theory’s commitments and potential and describe some simple simulation results which make progress in this regard. Though the inquiry often problematizes the signalling theory, it also shows that it should not be dismissed outright, and that it makes predictions which are apt for empirical testing. (shrink)

In this article, we reflect on the use of formal methods in the philosophy of science. These are taken to comprise not just methods from logic broadly conceived, but also from other formal disciplines such as probability theory, game theory, and graph theory. We explain how formal modelling in the philosophy of science can shed light on difficult problems in this domain.

Computers are increasingly interactive. They are no more transformational systems producing a final output after a finite execution. Instead, they continuously react in time to external events that modify the course of computing execution. While philosophers have been interested in conceptualizing computers for a long time, they seem to have paid little attention to the specificities of interactive computing. We propose to tackle this issue by surveying the literature in theoretical computer science, where one can find explicit proposals for a (...) model of interactive computing. In that field, the formal modelling of interactive computing systems has been brought down to whether the new interaction models are reducible to Turing Machines. There are three areas where interaction models are framed. The comparison between TMs and interactive system models is at stake in all of them. These areas are namely some works on concurrency by Milner, on Reactive Turing Machines, and on interaction as a new computing paradigm. For each of the three identified models, we present its motivation, sum up its account for interaction and its legacy, and point out issues regarding the understanding of computers. The survey shows difficulties for epistemologists. The reason is that these analyses focus on the formal equivalence between interactive models of computation and classic ones. Such a project is different from addressing how a computing machine can be interactive: in other words, which mechanisms allow it. (shrink)

The First International and Interdisciplinary Conference on Modelling and Using Context, Rio de Janeiro, January 1997, gave rise to the present book, which contains a selection of the papers presented there, thoroughly refereed and revised. The treatment of contexts as bona fide objects of logical formalisation has gained wide acceptance, following the seminal impetus given by McCarthy in his Turing Award address. The field of natural language offers a particularly rich variety of examples and challenges to researchers concerned with the (...) formal modelling of context, and several chapters in the volume deal with contextualisation in the setting of natural language. Others adopt a purely formal-logical viewpoint, seeking to develop general models of even wider applicability. The 12 chapters are organised in three groups: formalisation of contextual information in natural language understanding and generation, the application of context in mechanised reasoning domains, and novel non-classical logics for contextual application. (shrink)

This paper presents an exercise in the formalization of political principles, by taking as its theme the concept of distributive justice that Karl Marx advanced in his Critique of the Gotha Programme. We first summarize the content of the Critique of the Gotha Programme. Next, we transcribe the core of Marx’s presentation of the concept of distributive justice. Following, we present our formalization of Marx’s conception. Then, we make use of that formal analysis to confront Marx’s principle of distributive (...) justice with John Rawls’ conception of justice as fairness, and the principles of distributive justice that derive from it. Finally, we discuss methodological issues relative to, and implications of, the way of formalizing political principles introduced here. (shrink)

Rosen's modelling relations constitute a conceptual schema for the understanding of the bidirectional process of correspondence between natural systems and formal symbolic systems. The notion of formal systems used in this study refers to information structures constructed as algebraic rings of observable attributes of natural systems, in which the notion of observable signifies a physical attribute that, in principle, can be measured. Due to the fact that modelling relations are bidirectional by construction, they admit a precise categorical formulation (...) in terms of the category-theoretic syntactic language of adjoint functors, representing the inverse processes of information encoding/decoding via adjunctions. As an application, we construct a topological modelling schema of complex systems. The crucial distinguishing requirement between simple and complex systems in this schema is reflected with respect to their rings of observables by the property of global commutativity. The global information structure representing the behaviour of a complex system is modelled functorially in terms of its spectrum functor. An exact modelling relation is obtained by means of a complex encoding/decoding adjunction restricted to an equivalence between the category of complex information structures and the category of sheaves over a base category of partial or local information carriers equipped with an appropriate topology. (shrink)

In this paper, we present two ways of modelling every epistemic formal conditional commitment that involves (at most) three key epistemic attitudes: acceptance, rejection and neither acceptance nor rejection. The first one consists of adopting the plurality of every mixed Strong Kleene logic (along with an epistemic reading of the truth-values), and the second one involves the use of a unified system of six-sided inferences, named 6SK, that recovers the validities of each mixed Strong Kleene logic. We also introduce (...) a sequent calculus that is sound and complete with respect to both approaches. We compare both accounts, and finally, we suggest that the plurality of Strong Kleene logic as well as the general framework 6SK are linked to formal epistemic norms via bridge principles. (shrink)

This paper contributes to the philosophical accounts of generalisation in formal modelling by introducing a conceptual framework that allows for recognising generalisations that are epistemically beneficial in the sense of contributing to the truth of a model result or component. The framework is useful for modellers themselves because it is shown how to recognise different kinds of generalisation on the basis of changes in model descriptions. Since epistemically beneficial generalisations usually de-idealise the model, the paper proposes a reformulation of (...) the well-known distinction between abstraction and idealisation. A reformulated notion of abstraction is needed because the extant accounts yield wrong judgments when model-modifications introduce implicit assumptions. (shrink)

Conceptual models are descriptions of our ideas about a problem, used to shape the implementation of a solution to it. Everyone who builds complex information systems uses such models - be they requirements analysts, knowledge modellers or software designers - but understanding of the pragmatics of model design tends to be informal and parochial. Lightweight uses of logic can add precision without destroying the intuitions we use to interpret our descriptions. Computing with logic allows us to make use of this (...) precision in providing automated support tools. Modern information scientists need to know what these methods are for and may need to build their own. This book gives you a place to begin. Where do you start when building models in a precise language like logic? One way is by following standard paradigms for design and adapting these to your needs. Some of these come from an analysis of existing informal notations. Others are from within logic itself. We take you through a sample of these, from more commonplace styles of formal modelling to non-standard methods such as techniques editing and argumentation. Each of these provides a window onto broader areas of applied logic and gives you a basis for adapting the method to your own needs. (shrink)

This paper deals with causal analysis in the social sciences. We first present a conceptual framework according to which causal analysis is based on a rationale of variation and invariance, and not only on regularity. We then develop a formal framework for causal analysis by means of structural modelling. Within this framework we approach causality in terms of exogeneity in a structural conditional model based which is based on (i) congruence with background knowledge, (ii) invariance under a large variety (...) of environmental changes, and (iii) model fit. We also tackle the issue of confounding and show how latent confounders can play havoc with exogeneity. This framework avoids making untestable metaphysical claims about causal relations and yet remains useful for cognitive and action-oriented goals. (shrink)

Mazur & Booth (1998) (M&B) suggested that high testosterone (T) relates to status, dominance, and (anti-) social behaviour. However, low T also relates to status and to formal dominance. The General Trait Covariance (GTC) model predicts both relations under the assumption that high and low T modulates the genotype in ways that enforce the development of almost polar covariant patterns of body, brain, intellectual, and personality traits, irrespective of race. The precise modelling of these dose-dependent molecular body-intelligence-personality-behaviour relations requires (...) that causes, mechanisms, and effects enjoy equal operational standing. (shrink)

Philosophers, linguists and others interested in problems concerning natural language frequently employ tools from logic and model theory. The question arises as to the proper interpretation of the formal methods employed—of the relationship between, on the one hand, the formal languages and their set-theoretic models and, on the other hand, the objects of ultimate interest: natural language and the meanings and truth conditions of its constituent words, phrases and sentences. Two familiar answers to this question are descriptivism and (...) instrumentalism. More recently, a third answer has been proposed: the logic as modelling view. This paper seeks to clarify and assess this view of logic. The conclusion is that we can successfully adopt the modelling perspective on a given piece of logical machinery only if we have to hand some other machinery to which we take the descriptive attitude. Thus, logic as modelling is not a full-fledged alternative to the descriptive view— for it cannot stand alone: it can at best be an addition to the descriptive perspective. The paper first presents the argument in a general, abstract form, before working through a detailed case study. The case examined is the one with respect to which the logic as modelling view has been developed in the greatest detail in the literature: the case of fuzzy model theory as an account of vagueness in natural language. (shrink)

Process modeling is ubiquitous in business and industry. While a great deal of effort has been devoted to the formal and philosophical investigation of processes, surprisingly little research connects this work to real world process modeling. The purpose of this paper is to begin making such a connection. To do so, we first develop a simple mathematical model of activities and their instances based upon the model theory for the NIST Process Specification Language (PSL), a simple language (...) for describing these entities, and a semantics for the latter in terms of the former, and a set of axioms for the semantics based upon the NIST Process Specification Language (PSL). On the basis of this foundation, we then develop a general notion of a process model, and an account of what it is for such a model to be realized by a collection of events. (shrink)

In this paper, I utilise the growing literature on scientific modelling to investigate the nature of formal semantics from the perspective of the philosophy of science. Specifically, I incorporate the inferential framework proposed by Bueno and Colyvan : 345–374, 2011) in the philosophy of applied mathematics to offer an account of how formal semantics explains and models its data. This view produces a picture of formal semantic models as involving an embedded process of inference and representation applying (...) indirectly to linguistic phenomena. The final aim of the paper is directed at proposing a novel account of the syntax–semantics interface while shedding light on empty categories, semantically null forms, underspecified content and compositionality as a whole. (shrink)

Emergence is defined as a process which cannot be described by a fixed model, consisting of invariant distinctions. Hence emergence must be described by a meta‐model, representing the transition of one model to another one by means of a distinction dynamics. The dynamics of distinctions is based on the processes of variation and selection, resulting in an invariant distinction, which constrains the variety and thus defines a new system. A classification of emergence processes is proposed, based on the following criteria: (...) amount of variety, internality/ externality of variation and selection, number of levels, and contingency of constraint. It is argued that traditional formal and computational models are incapable of representing the more general types of emergence, but that it is possible to generalize them on the basis of the dynamics of distinctions. (shrink)

According to one tradition in realist philosophy, 'truthmaking' amounts to necessitation. That is, an object x is a truthmaker for the claim A if x exists, and the existence of x necessitates the truth of A. I argued in my paper "Truthmakers, Entailment and Necessity" [14], that if we wish to use this account of truthmaking, we ought understand the entailment connective "=>" in such a claim as a relevant entailment, in the tradition of Anderson and Belnap and their co-workers (...) [1, 2, 8, 11]. Furthermore, I proposed a number of theses about truthmaking as necessitation. The most controversial of these is the disjunction thesis: x makes a disjunction A v B true if and only if it makes one of the disjuncts (A or B) true. That paper left one important task unfinished. I did not explain how the theses about truthmaking could be true together. In this paper I give a consistency proof, by providing a model for the theses of truthmaking in my earlier paper. This result does two things. First, it shows that the theses of truthmaking are jointly consistent. Second, it provides an independently philosophically motivated formal model for relevant logics in the 'possible worlds' tradition of Routley and Meyer [8, 16, 17]. (shrink)

This paper discusses the epistemological and methodological bases of a scientific theory of meaning and proposes a detailed version of a formal theory of argumentation based on Anscombre and Ducrot's conception. Argumentation is shown to be a concept which is not exclusively pragmatic, as it is usually believed, but has an important semantic body. The bridge between the semantic and pragmatic aspects of argumentation consists in a set of gradual inference rules, called topoi, on which the argumentative movement is (...) based. The content of each topos is determined at the pragmatic level, while the constraints on the forms of the topoi attached to a sentence are determined at the semantic level. Applications and possible applications toartificial intelligence and to cognitive sciences are discussed. In particular, the gradual models used to account for argumentation are shown to be extremely promising for Knowledge management, a discipline which includes knowledge acquisition, knowledge representation, transmission of knowledge (communication, interfaces, etc.), knowledge production (decision help, reasoning, etc.). A first formal model is presented and discussed: it is shown in details how it accounts for most of the argumentative features of sentences containing but, little and a little, and how it can be extended to describe sentences containing other argumentative connectives. However, this model is shown to be too simple and to violate the compositionality principle, which is shown, in the first section, to bean important methodological principle for any scientific theory. After a detailed analysis of the possible reasons for this violation, an improved model is proposed and its adequacy is discussed. (shrink)

Conversation is one of the main contexts in which we are conducting inquiries. Yet, little attention has been paid so far in pragmatics or epistemology to the process of inquiry in conversation. In this paper, we propose to trigger such an investigation through the development of a formal modelling based on inquisitive pragmatics—a framework offering a semantic representation of questions and answers, along with an analysis of the pragmatic principles that govern questioning and answering moves in conversations geared towards (...) information exchange. Our starting observation is that an interrogative inquiry in a conversation takes the form of a finite sequence of questioning and answering steps, and appears thereby as an inherently temporal process. The central notion of interrogative protocol introduced in this paper precisely aims to capture the temporal dimension of inquiry. Interrogative protocols are defined as branching-time tree structures encoding all the possible sequences of questioning and answering steps—i.e., all the possible inquiry paths—that can subsequently occur in a starting conversational situation in accordance with the principles of inquisitive pragmatics. They provide us with a formal environment to define and investigate the epistemological notions of interrogative inquiry and interrogative consequence in conversational contexts. One of the main interests of the resulting framework is to enable a formal investigation of central epistemological issues relative to interrogative inquiry under the form of computational problems. We frame three key inquiry problems along this line, and we then propose an algorithmic procedure for solving them in the restricted case where the inquirer has at her disposal a finite number of questions in her inquiry. We conclude by relating our approach to Wiśniewski’s Erotetic Search Scenarios and Hintikka’s Interrogative Model of Inquiry. (shrink)

An essential aspect of conceptual data modeling methodologies is the language’s expressiveness so as to represent the subject domain as precise as possible to obtain good quality models and, consequently, software. To gain better insight in the characteristics of the main conceptual modeling languages, we conducted a comparison between ORM, ORM2, UML, ER, and EER with the aid of Description Logic languages of the DLR family and the new formally defined generic conceptual data modeling language CMcom that (...) is based on DLRifd. ORM, ER, EER, and UML class diagrams are proper fragments of ORM2 and CMcom has the most expressive common denominator with these languages. CMcom simplifies prospects for automated, online, interoperability among the considered languages so that modelers not only can continue using their preferred modeling language yet be compatible with the other ones, but also have a common ground that eases database and software integration based on commonly used conceptual data models. (shrink)

Understanding the mechanisms and the time and spatial evolution of penumbra following an ischemic stroke is crucially important for developing therapeutics aimed at preventing this area from evolving towards infarction. To help in integrating the available data, we decided to build a formal model. We first collected and categorised the major available evidence from animal models and human observations and summarized this knowledge in a flow-chart with the potential key components of an evolving stroke. Components were grouped in ten (...) sub-models that could be modelled and tested independently: the sub-models of tissue reactions, ionic movements, oedema development, glutamate excitotoxicity, spreading depression, NO synthesis, inflammation, necrosis, apoptosis, and reperfusion. Then, we figured out markers, identified mediators and chose the level of complexity to model these sub-models. We first applied this integrative approach to build a model based on cytotoxic oedema development following a stroke. Although this model includes only three sub-models and would need to integrate more mechanisms in each of these sub-models, the characteristics and the time and spatial evolution of penumbra obtained by simulation are qualitatively and, to some extent, quantitatively consistent with those observed using medical imaging after a permanent occlusion or after an occlusion followed by a reperfusion. (shrink)

This paper proposes two formal models for understanding real-life dialogues, aimed at capturing argumentative structures performatively enacted during conversations. In the course of the investigation, two types of discourse with a high degree of well-structured argumentation were chosen: moral debate and financial communication. The research project found itself confronted by a need to analyse, structure and formally describe large volumes of textual data, where this called for the application of computational tools. It is expected that the results of the (...) proposed research will make a contribution to formal systems modelling and the evaluation of communication from the point of view of argument soundness. (shrink)

Current research in Explainable AI includes post-hoc explanation methods that focus on building transparent explaining agents able to emulate opaque ones. Such agents are naturally required to be accurate and trustworthy. However, what it means for an explaining agent to be accurate and trustworthy is far from being clear. We characterize accuracy and trustworthiness as measures of the distance between the formal properties of a given opaque system and those of its transparent explanantes. To this aim, we extend Probabilistic (...) Computation Tree Logic with operators to specify degrees of accuracy and trustworthiness of explaining agents. We also provide a semantics for this logic, based on a multi-agent structure and relative model-checking algorithms. The paper concludes with a simple example of a possible application. (shrink)

We show how to embed a framework for multilateral negotiation, in which a group of agents implement a sequence of deals concerning the exchange of a number of resources, into linear logic. In this model, multisets of goods, allocations of resources, preferences of agents, and deals are all modelled as formulas of linear logic. Whether or not a proposed deal is rational, given the preferences of the agents concerned, reduces to a question of provability, as does the question of whether (...) there exists a sequence of deals leading to an allocation with certain desirable properties, such as maximising social welfare. Thus, linear logic provides a formal basis for modelling convergence properties in distributed resource allocation. (shrink)

In philosophy, and especially in ethics, reflective equilibrium (RE) is often considered a powerful method for obtaining beliefs that mutually support each other, are justified by evidence, and are backed by good reasons. Beisbart, Betz, and Brun (2021) have introduced a formal model of reflective equilibrium based on the theory of dialectical structures Betz (2013), which they use as a methodological tool to understand the method of reflective equilibrium better. This report is an outcome of the research project 'How (...) far does Reflective Equilibrium Take us? Investigating the Power of a Philosophical Method' and summarizes the findings of assessing the model thoroughly by numerical investigation. We simulate RE processes for a broad spectrum of model parameters and initial conditions and use four different model variants (including the original model). We analyze the dependence of simulation results on different parameters and assess the models' conduciveness towards consistency, and ability to reach global optima and full RE states. The results show that the models' behavior depends crucially on the specifics of the simulation setup. We can, therefore, not draw any general conclusions about the overall performance of the model variants. Rather, the specifics of the context in which an RE model is used must be considered to choose a specific model. Finally, we identify some critical knowledge gaps we cannot close with this report that call for further research into RE modelling. (shrink)

FOIS is the flagship conference of the International Association for Ontology and its Applications, a non-profit organization which promotes interdisciplinary research and international collaboration at the intersection of philosophical ontology, linguistics, logic, cognitive science, and computer science. This book presents the papers delivered at FOIS 2023, the 13th edition of the Formal Ontology in Information Systems conference. The event was held as a sequentially-hybrid event, face-to-face in Sherbrooke, Canada, from 17 to 20 July 2023, and online from 18 to (...) 20 September 2023. In total, 62 articles from 19 different countries were submitted, out of which 25 were accepted for inclusion in the conference and for publication; corresponding to an acceptance rate of 40 percent. The contributions are separated into the book’s three sections: (1) Foundational ontological issues; (2) Methodological issues around the development, alignment, verification and use of ontologies; and (3) Domain ontologies and ontology-based applications. In these sections, ontological aspects from a wide variety of fields are covered, primarily from various engineering domains including cybersecurity, manufacturing, petroleum engineering, and robotics, but also extending to the humanities, social sciences, medicine, and dentistry. A noticeable trend among the contributions in this edition of the conference is the recognition that improving the tools to analyze, align, and improve ontologies is of paramount importance in continuing to advance the field of formal ontology. The book will be of interest to all formal and applied ontology researchers, and to those who use formal ontologies and information systems as part of their work. (shrink)

A cutting-edge survey of formal methods directed specifically at dealing with the deep mathematical problems engendered by the study of developing systems, in particular dealing with developing phase spaces, changing components, structures and functionalities, and the problem of emergence. Several papers deal with the modelling of particular experimental situations in population biology, economics and plant and muscle developments in addition to purely theoretical approaches. Novel approaches include differential inclusions and viability theory, growth tensors, archetypal dynamics, ensembles with variable structures, (...) and complex system models. The papers represent the work of theoreticians and experimental biologists, psychologists and economists. The areas covered embrace complex systems, the development of artificial life, mathematics, computer science, biology and psychology. (shrink)

In formal epistemology, we use mathematical methods to explore the questions of epistemology and rational choice. What can we know? What should we believe and how strongly? How should we act based on our beliefs and values? We begin by modelling phenomena like knowledge, belief, and desire using mathematical machinery, just as a biologist might model the fluctuations of a pair of competing populations, or a physicist might model the turbulence of a fluid passing through a small aperture. Then, (...) we explore, discover, and justify the laws governing those phenomena, using the precision that mathematical machinery affords. For example, we might represent a person by the strengths of their beliefs, and we might measure these using real numbers, which we call credences. Having done this, we might ask what the norms are that govern that person when we represent them in that way. How should those credences hang together? How should the credences change in response to evidence? And how should those credences guide the person’s actions? This is the approach of the first six chapters of this handbook. In the second half, we consider different representations—the set of propositions a person believes; their ranking of propositions by their plausibility. And in each case we ask again what the norms are that govern a person so represented. Or, we might represent them as having both credences and full beliefs, and then ask how those two representations should interact with one another. This handbook is incomplete, as such ventures often are. Formal epistemology is a much wider topic than we present here. One omission, for instance, is social epistemology, where we consider not only individual believers but also the epistemic aspects of their place in a social world. Michael Caie’s entry on doxastic logic touches on one part of this topic, but there is much more. Relatedly, there is no entry on epistemic logic, nor any on knowledge more generally. There are still more gaps. These omissions should not be taken as ideological choices. This material is missing, not because it is any less valuable or interesting, but because we v failed to secure it in time. Rather than delay publication further, we chose to go ahead with what is already a substantial collection. We anticipate a further volume in the future that will cover more ground. Why an open access handbook on this topic? A number of reasons. The topics covered here are large and complex and need the space allowed by the sort of 50 page treatment that many of the authors give. We also wanted to show that, using free and open software, one can overcome a major hurdle facing open access publishing, even on topics with complex typesetting needs. With the right software, one can produce attractive, clear publications at reasonably low cost. Indeed this handbook was created on a budget of exactly £0 (≈ $0). Our thanks to PhilPapers for serving as publisher, and to the authors: we are enormously grateful for the effort they put into their entries. (shrink)

In formal semantics, structure is treated as the essential ingredient in the creation of sentence meaning from individual word meaning. This book introduces some of the foundational concepts, principles and techniques in the formal semantics of natural language and outlines the mathematical principles that underlie linguistics meaning. Using English examples, Yoad Winter presents the most useful tools and concepts of formal semantics in an accessible style and includes a variety of practical exercises so that readers can learn (...) to utilize these tools effectively. For readers with an elementary background in set theory and linguistics or with an interest in mathematical modelling, this fascinating study is an ideal introduction to natural language semantics. Designed as a quick yet thorough introduction to one of the most vibrant areas of research in modern linguistics today this volume reveals the beauty and elegance of the mathematical study of meaning. (shrink)

This paper's purpose is to set forth the conditions of explanation in the domain of formal modelling of social action. Explanation is defined as an adequate account of the underlying factors bringing about a phenomenon. The modelling of a social phenomenon can claim explanatory value in this sense if the following two conditions are fulfilled. (1) The generative mechanisms involved translate the effects of real factors abstracted from their phenomenal context, not those of purely ideal ones. (2) The explanatory (...) hypotheses, which account for the effects of explanatory factors, and the purely descriptive hypotheses, which introduce conceptual simplifications and summarise complex secondary mechanisms, are relatively independent from each other with regard to the phenomenon represented. This condition subjects the model to testing by alternatives through the development of purely descriptive hypotheses in the sense of explanatory or analytical realism. (shrink)

With a few notable exceptions formal semantics, as it originated from the seminal work of Richard Montague, Donald Davidson, Max Cresswell, David Lewis and others, in the late sixties and early seventies of the previous century, does not consider Wittgenstein as one of its ancestors. That honour is bestowed on Frege, Tarski, Carnap. And so it has been in later developments. Most introductions to the subject will refer to Frege and Tarski (Carnap less frequently) —in addition to the pioneers (...) just mentioned, of course— , and discuss the main elements of their work that helped shape formal semantics in some detail. But Wittgenstein is conspicuously absent whenever the history of the subject is mentioned (usually briefly, if at all). Of course, if one thinks of Wittgenstein’s later work, this is obvious: nothing, it seems, could be more antithetic to what formal semantics aims for and to how it pursues those aims than the views on meaning and language that Wittgenstein expounds in, e.g., Philosophical Investigations, with its insistence on particularity and diversity, and its rejection of explanation and formal modelling. But what about his earlier work, the Tractatus (henceforth )? At first sight, that seems much more congenial, as it develops a conception of language and meaning that is both general and uniform, explanatory.. (shrink)

In the court of law, a person can be punished for attempting to commit a crime. An open issue in the study of Artificial Intelligence and Law is whether the law of attempts could be formally modelled. There are distinct legal rules for determining attempted crime whereas the last-act rule (also called proximity rule) represents the strictest approach. In this paper, we provide a formal model of the last-act rule using structured argumentation.

This paper aims to model multilevel interdependencies in complex organisational systems and proposes application for resilience analysis. Most of the existing research studied interdependencies only at the single-level and overlooked their multilevel character. In response to this gap, we propose a multilevel approach to better comprehend the complexity of interdependencies in organisational systems. More specifically, the study focuses on how interdependencies are shaped across multiple organisational levels. To understand the research problem, we use multilevel and social network theories to elaborate (...) the concept at five organisational levels, namely, individual, intraunit, interunit, intraorganisational, and interorganisational. Further, we show the application of multilevel interdependencies into analysis of organisational resilience. To this end, we construct a multiplex model of a real world organisational system that comprises formal and informal relations of different social exchange strength. Using the agent-based simulations of the organisational system, we investigate the relations between organisational interdependencies and organisational performance in normal and disrupted conditions. With the results, we argue that managing multilevel interdependencies is crucial to reduce vulnerability of organisational systems. By introducing the multilevel conceptualisation of interdependencies and presenting their influence on organisational resilience, we hope to pave a path to managing the complexity of interdependencies and strategic resilience enhancement in organisational systems. (shrink)

James Franklin has argued that the formal, mathematical sciences of complexity — network theory, information theory, game theory, control theory, etc. — have a methodology that is different from the methodology of the natural sciences, and which can result in a knowledge of physical systems that has the epistemic character of deductive mathematical knowledge. I evaluate Franklin’s arguments in light of realistic examples of mathematical modelling and conclude that, in general, the formal sciences are no more able to (...) guarantee certainty than the natural sciences. Yet the formal sciences are characterized by a ‘domain-independence’ that is philosophically interesting, and I argue that it is this property that Franklin actually employs to distinguish the formal from the natural sciences. I use Einstein’s ‘principle’/‘constructive’ theory distinction to contrast the domain-independence of physical theories with the domain-independence of formal mathematical theories, and show how both kinds of domain-independence function to generate the domain-independence that is observed in the complex systems sciences. © 1999 Elsevier Science Ltd. All rights reserved. (shrink)

Introduction to modelling and validation -- Non-hierarchical coloured petri nets -- CPN ML programming -- Formal definition of non-hierarchical coloured petri nets -- Hierarchical coloured petri nets -- Formal defintion of hierarchical coloured petri nets -- State spaces and behavioural properties -- Advanced state space methods -- Formal definition of state spaces and behavioural properties -- Timed coloured petri nets -- Formal definition of timed coloured petri nets -- Simulation-based performance analysis -- Behavioural visualisation -- Examples (...) of industrial applications -- Teaching coloured petri nets. (shrink)

Biologists rely extensively on the iterated Prisoner's Dilemma game to model reciprocal altruism. After examining the informal conditions necessary for reciprocal altruism, I argue that formal games besides the standard iterated Prisoner's Dilemma meet these conditions. One alternate representation, the modified Prisoner's Dilemma game, removes a standard but unnecessary condition; the other game is what I call a Cook's Dilemma. We should explore these new models of reciprocal altruism because they predict different stability characteristics for various strategies; for instance, (...) I show that strategies such as Tit-for-Tat have different stability dynamics in these alternate models. (shrink)

The question whether natural language can be captured in a formal system has been argued at length, and both a positive and a negative answer has been defended. The paper investigates the main lines of argument for both, and argues that the stalemate that appears to have been reached is an indication that the question itself rests on a wrong conception of the relation between natural languages and formal languages, and hence of the methodological status of formal (...) modelling of natural language. (shrink)

If well-designed, the results of a Randomised Clinical Trial can justify a causal claim between treatment and effect in the study population; however, additional information might be needed to carry over this result to another population. RCTs have been criticized exactly on grounds of failing to provide this sort of information Evidence, inference and enquiry. Oxford University Press, New York, 2011), as well as to black-box important details regarding the mechanisms underpinning the causal law instantiated by the RCT result. On (...) the other side, so-called In Silico Clinical Trials face the same criticisms addressed against standard modelling and simulation techniques, and cannot be equated to experiments Philosophy of molecular medicine: foundational issues in research and practice, Routledge, New York, 2017; Parker in Synthese 169:483–496, 2009; Parke in Philos Sci 81:516–536, 2014; Diez Roux in Am J Epidemiol 181:100–102, 2015 and related discussions in Frigg and Reiss in Synthese 169:593–613, 2009; Winsberg in Synthese 169:575–592, 2009; Beisbart and Norton in Int Stud Philos Sci 26:403–422, 2012). We undertake a formal analysis of both methods in order to identify their distinct contribution to causal inference in the clinical setting. Britton et al.’s study :E2098–E2105, 2013) on the impact of ion current variability on cardiac electrophysiology is used for illustrative purposes. We deduce that, by predicting variability through interpolation, ISCTs aid with problems regarding extrapolation of RCTs results, and therefore in assessing their external validity. Furthermore, ISCTs can be said to encode “thick” causal knowledge —as opposed to “thin” difference-making information inferred from RCTs. Hence, ISCTs and RCTs cannot replace one another but rather, they are complementary in that the former provide information about the determinants of variability of causal effects, while the latter can, under certain conditions, establish causality in the first place. (shrink)

Should research projects involving epidemiological modelling be subject to ethical scrutiny and peer review prior to publication? Mathematical modelling had considerable impacts during the COVID-19 pandemic, leading to social distancing and lockdowns. Imperial College conducted research leading to the website publication of a paper, Report 9, on non-pharmaceutical interventions (NPIs) and COVID-19 mortality demand dated 16th March 2020, arguing for a Government policy of non-pharmaceutical interventions (e.g. lockdowns, social distancing, mask wearing, working from home, furlough, school closures, reduced family interaction (...) etc.) to counter COVID 19. Enquiries and Freedom of Information requests to the institution indicate that there was no formal ethical committee review of this specific research, nor was there any peer review prior to their online publication of Report 9. This paper considers the duties placed upon researchers, institutions and research funders under the UK ‘Concordat to Support Research Integrity’ (CSRI), across various bioethical domains, and whether ethical committee scrutiny should be required for this research. (shrink)

This paper has four aims. First it distinguishes two kinds of philosophical accounts of the ‘formal’ features of rights: models and theories. Models outline the ‘conceptually basic’ types of rights (if indeed a given model deems there to be more than one), their differences, and their relationships with duties, liabilities, etc. Theories of rights posit a supposed ultimate purpose for all rights and provide criteria for determining what counts as ‘a right’ in the first place. Second, the paper argues (...) that Monistic rights models (ones positing only a single basic type of right) are under-inclusive. They wrongly exclude and cannot explain relevant data, i.e., ordinary and legal linguistic practices. The third aim is to show that certain Pluralistic models are over-inclusive in terms of what they count as ‘rights’. Fourth, the paper begins to touch upon, but does not provide, criteria for determining what counts as ‘a right’. Two candidate factors will be addressed. (shrink)