Taxonomy Based modeling was applied to describe drivers’ mental models of variable message signs (VMS’s) displayed on expressways. Progress in road telematics has made it possible to introduce variable message signs (VMS’s). Sensors embedded in the carriageway every 500m record certain variables (speed, flow rate, etc.) that are transformed in real time into “driving times” to a given destination if road conditions do not change.VMS systems are auto-regulative Man-Machine (AMMI) systems which incorporate a model of the user: if the (...) traffic flow is too high, then drivers should choose alternative routes. In so doing, the traffic flow should decrease. The model of the user is based on suppositions such as: people do not like to waste time, they fully understand the displayed messages, they trust the displayed values, they know of alternative routes. However, people also have a model of the way the system functions. And if they do not believe the contents of the message, they will not act as expected.We collected data through interviews with drivers using the critical incidents technique (Flanagan, 1985). Results show that the mental models that drivers have of the way the VMS system works are various but not numerous and that most of them differ from the“ideal expert” mental model. It is clear that users don’t have an adequate model of how the VMS system works and that VMS planners have a model of user behaviour that does not correspond to the behaviour of the drivers we interviewed. Finally, Taxonomy Based Modeling is discussed as a tool for mental model remediation. (shrink)

This book discusses how scientific and other types of cognition make use of models, abduction, and explanatory reasoning in order to produce important, innovative, and possibly creative changes in theories and concepts. Gathering revised contributions presented at the international conference on Model-Based Reasoning (MBR023), held on June 7–9, 2023 in Rome, Italy, the book addresses various intertwined topics ranging from the epistemology and applications of models also concerning the problem of knowledge production and scientific methodology (information (...) visualization, experimental methods, and design) to the analysis of their role in cognition, decision-making, also with respect to social implications. The problem of model-based cognition is also illustrated taking advantage of recent results regarding problem-solving, abduction, and logic, paying attention to a critique of the dominant and received approaches, to the aim of fostering new discussions and stimulate new ideas. All in all, the book provides researchers and graduate students in the fields of applied philosophy, epistemology, cognitive science, and artificial intelligence alike with an authoritative snapshot of the latest theories and applications of model-based reasoning. (shrink)

The existence of non-standard numbers in first-order arithmetics is a semantic obstacle for modelling our arithmetical skills. This article argues that so far there is no adequate approach to overcome such a semantic obstacle, because we can also find out, and deal with, non-standard elements in Turing machines.

We present preliminary results on modelling structure of solutions to a task involving abductive reasoning. Research data were gathered using our new tool—Find Out, which has been designed in order to account empirically for abduction relatively close to everyday reasoning processes, with the necessary level of procedure standardization. The tool enables to capture abduction as a compound form of reasoning, from both product and process perspective. Find Out is set up as a game that requires playing the (...) role of an investigator seeking an explanation of what has happened in the presented enigmatic situation. The task consists of three time-limited stages that require different reasoning activities. In the paper, we present quantitative models of structures of solutions to the task proposed by the subjects in the form of situational graphs. We present also some ideas concerning qualitative characteristics of these solutions. (shrink)

This paper presents an attempt to bridge the gap between logical and cognitive treatments of strategic reasoning in games. There have been extensive formal debates about the merits of the principle of backward induction among game theorists and logicians. Experimental economists and psychologists have shown that human subjects, perhaps due to their bounded resources, do not always follow the backward induction strategy, leading to unexpected outcomes. Recently, based on an eye-tracking study, it has turned out that even human subjects (...) who produce the outwardly correct ‘backward induction answer’ use a different internal reasoning strategy to achieve it. The paper presents a formal language to represent different strategies on a finer-grained level than was possible before. The language and its semantics help to precisely distinguish different cognitive reasoning strategies, that can then be tested on the basis of computational cognitive models and experiments with human subjects. The syntactic framework of the formal system provides a generic way of constructing computational cognitive models of the participants of the Marble Drop game. (shrink)

The emergence of new computational media is radically changing the practices of science, particularly in the way computational models are built and used to understand and engineer complex biological systems. These new practices present a novel variation of model-based reasoning, based on dynamic and opaque models. A new cognitive account of MBR is needed to understand the nature of this practice and its implications. To develop such an account, I first outline two cases where the building and (...) use of computational models led to discoveries. A theoretical model of the possible cognitive and neural mechanisms underlying such discoveries is then presented, based on the way the body schema is extended during tool use. This account suggests that the process of building the computational model gradually ‘incorporates’ the external model as a part of the internal imagination system, similar to the way tools are incorporated into the body schema through their active use. A central feature of this incorporation account is the critical role played by tacit and implicit reasoning. Based on this account, I examine how computational modeling would change model-based reasoning in science and science education. (shrink)

Barrio et al. (_Journal of Philosophical Logic_, _49_(1), 93–120, 2020 ) and Pailos (_Review of Symbolic Logic_, _2020_(2), 249–268, 2020 ) develop an approach to define various metainferential hierarchies on strong Kleene models by transferring the idea of distinct standards for premises and conclusions from inferences to metainferences. In particular, they focus on a hierarchy named the $\mathbb {S}\mathbb {T}$ -hierarchy where the inferential logic at the bottom of the hierarchy is the non-transitive logic ST but where (...) each subsequent metainferential logic ‘says’ about the former logic that it is transitive. While Barrio et al. ( 2020 ) suggests that this hierarchy is such that each subsequent level ‘in some intuitive sense, more classical than’ the previous level, Pailos ( 2020 ) proposes an extension of the hierarchy through which a ‘fully classical’ metainferential logic can be defined. Both Barrio et al. ( 2020 ) and Pailos ( 2020 ) explore the hierarchy in terms of semantic definitions and every proof proceeds by a rather cumbersome reasoning about those semantic definitions. The aim of this paper is to present and illustrate the virtues of a proof-theoretic tool for reasoning about the $\mathbb {S}\mathbb {T}$ -hierarchy and the other metainferential hierarchies definable on strong Kleene models. Using the tool, this paper argues that each level in the $\mathbb {S}\mathbb {T}$ -hierarchy is non-classical to an equal extent and that the ‘fully classical’ metainferential logic is actually just the original non-transitive logic ST ‘in disguise’. The paper concludes with some remarks about how the various results about the $\mathbb {S}\mathbb {T}$ -hierarchy could be seen as a guide to help us imagine what a non-transitive metalogic for ST would tell us about ST. In particular, it teaches us that ST is from the perspective of ST as metatheory not only non-transitive but also transitive. (shrink)

This study examined the hypothesis that a key process in conditional reasoning with concrete premises involves on-line retrieval of information about potential alternate antecedents. Participants were asked to solve reasoning problems with causal conditional premises (If cause P then effect Q). These premises were inserted into short contexts. The availability of potential alternatives was varied from one context to another by adding statements that explicitly invalidated one or more of these alternatives (i.e., other causes that lead to the (...) effect Q). The invalidated alternatives differed in the degree of their semantic association to the consequent term (Q). The results show that the effect of invalidating one or more potential alternatives on the two uncertain logical forms, AC and DA, was largely determined by their relative associative strength. These results strongly support a model for conditional reasoning with causal premises that supposes that a key element in responding to the uncertain logical forms is on-line retrieval of at least one potential alternative antecedent. (shrink)

This article demonstrates that typical restrictions which are imposed in dialogical logic in order to recover first-order logical consequence from a fragment of natural language argumentation are also forthcoming from preference profiles of boundedly rational players, provided that these players instantiate a specific player type and compute partial strategies. We present two structural rules, which are formulated similarly to closure rules for tableaux proofs that restrict players' strategies to a mapping between games in extensive forms and proof trees. Both (...) rules are motivated from players' preferences and limitations; they can therefore be viewed as being player-self-imposable. First-order logical consequence is thus shown to result from playing a specific type of argumentation game. The alignment of such games with the normative model of the Pragma-dialectical theory of argumentation is positively evaluated. But explicit rules to guarantee that the argumentation game instantiates first-order logical consequence have now become gratuitous, since their normative content arises directly from players' preferences and limitations. A similar naturalization for non-classical logics is discussed. (shrink)

In this paper, the Carneades argumentation system is extended to represent a procedural view of inquiry in which evidence is marshalled to support or defeat claims to knowledge. The model is a sequence of moves in a collaborative group inquiry in which parties take turns making assertions about what is known or not known, putting forward evidence to support them, and subjecting these moves to criticisms. It is shown how this model of evaluating evidence in an inquiry is based on (...) a defeasible logic using forms of argument that admit exceptions. It is contended that reasoning from absence of knowledge is as important to inquiry as positive reasoning from evidence to knowledge. The philosophical conflict between this view of reasoning about knowledge and the true-belief-plus view is explored by airing objections and replies on both sides. (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)

There are several key ingredients common to the various forms of model-based reasoning considered in this book. The term ‘model’ comprises both internal and external representations. The models are intended as interpretations of target physical systems, processes, phenomena, or situations and are retrieved or constructed on the basis of potentially satisfying salient constraints of the target domain. The book’s contributors are researchers active in the area of creative reasoning in science and technology.

This article describes the use of continuous vector space models for reasoning with a formal knowledge base. The practical significance of these models is that they support fast, approximate but robust inference and hypothesis generation, which is complementary to the slow, exact, but sometimes brittle behaviour of more traditional deduction engines such as theorem provers.The article explains the way logical connectives can be used in semantic vector models, and summarizes the development of Predication-based Semantic Indexing, which (...) involves the use of Vector Symbolic Architectures to represent the concepts and relationships from a knowledge base of subject-predicate-object triples. Experiments show that the use of continuous models for formal reasoning is not only possible, but already demonstrably effective for some recognized informatics tasks, and showing promise in other traditional problem areas. Examples described in this article include: predicting new uses for existing drugs in biomedical informatics; removing unwanted meanings from search results in information retrieval and concept navigation; type inference from attributes; comparing words based on their orthography; and representing tabular data, including modelling numerical values.The algorithms and techniques described in this article are all publicly released and freely available in the Semantic Vectors open-source software package.1. (shrink)

Rationality and reason are often used as synonyms, although they are very different concepts. In this article we argue that rationality is the concept of reason that has been stripped of its human elements. Ancient and medieval philosophers such as Aristotle and Aquinas stressed that the concept of reason is composed of sensitive, discursive, and moral elements. Post-Enlightenment thinkers instead, building on the works of René Descartes and Isaac Newton, took these out and claimed that rationality must be based (...) on an external logic devoid of value-concepts such as perfection, harmony, meaning and aim (Koyré in From the closed world to the infinite universe, The Johns Hopkins University Press, Baltimore, 1957). The purpose of this essay is to highlight this shift in Western thought and its consequences for management theories. While explaining the ancient concept of reason in contrast with modern rationalism (Klein in: Williamson RB, Zuckerman E (eds) Jacob Klein—lectures and essays, St. John’s College Press, Annapolis, 1985), we aim at raising awareness of the differences between building a research programme (especially in business sciences like economics and management) on rationality or on reason. (shrink)

Based on a close study of benchmark examples in default reasoning, such as Nixon Diamond, Penguin Principle, etc., this paper provides an in depth analysis of the basic features of default reasoning. We formalize default inferences based on Modus Ponens for Default Implication, and mark the distinction between "local inferences"(to infer a conclusion from a subset of given premises) and "global inferences"(to infer a conclusion from the entire set of given premises). These conceptual analyses are captured by a (...) formal semantics that is built upon the set-selection function technique. A minimal logic system M of default reasoning that accommodates Modus Ponens for Default Implication and suitable for local inferences is proposed, and its soundness is proved. (shrink)

It is known that the full computation-tree logic CTL * is an important base logic for model checking. The bisimulation theorem for CTL* is known to be useful for abstraction in model checking. In this paper, the bisimulation theorems for two paraconsistent four-valued extensions 4CTL* and 4LCTL* of CTL* are shown, and a translation from 4CTL* into CTL* is presented. By using 4CTL* and 4LCTL*, inconsistency-tolerant and spatiotemporal reasoning can be expressed as a model checking framework.

This paper studies a family of monotonic extensions of first-order logic which we call modulated logics, constructed by extending classical logic through generalized quantifiers called modulated quantifiers. This approach offers a new regard to what we call flexible reasoning. A uniform treatment of modulated logics is given here, obtaining some general results in model theory. Besides reviewing the “Logic of Ultrafilters”, which formalizes inductive assertions of the kind “almost all”, two new monotonic logical systems are proposed (...) here, the “Logic of Many” and the “Logic of Plausibility”, that characterize assertions of the kind “many”, and “for a good number of”. Although the notion of simple majority (“more than half”) can be captured by means of a modulated quantifier semantically interpreted by cardinal measure on evidence sets, it is proven that this system, although sound, cannot be complete if checked against the intended model. This justifies the interest on a purely qualitative approach to this kind of quantification, what is guaranteed by interpreting the modulated quantifiers as notions of families of principal filters and reduced topologies, respectively. We prove that both systems are conservative extensions of classical logic that preserve important properties, such as soundness and completeness. Some additional perspectives connecting our approach to flexible reasoning through modulated logics to epistemology and social choice theory are also discussed. (shrink)

One of the most important developments over the last twenty years both in logic and in Artificial Intelligence is the emergence of so-called non-monotonic logics. These logics were initially developed by McCarthy [10], McDermott & Doyle [13], and Reiter [17]. Part of the original motivation was to provide a formal framework within which to model cognitive phenomena such as defeasible inference and defeasible knowledge representation, i.e., to provide a formal account of the fact that reasoners can reach conclusions tentatively, (...) reserving the right to retract them in the light of further information. (shrink)

By action model, we understand any logic-based representation of effects and executability preconditions of individual actions within a certain domain. In the context of artificial intelligence, such models are necessary for planning and goal-oriented automated behaviour. Currently, action models are commonly hand-written by domain experts in advance. However, since this process is often difficult, time-consuming, and error-prone, it makes sense to let agents learn the effects and conditions of actions from their own observations. Even though the research (...) in the area of action learning, as a certain kind of inductive reasoning, is relatively young, there already exist several distinctive action learning methods. We will try to identify the collection of the most important properties of these methods, or challenges that they are trying to overcome, and briefly outline their impact on practical applications. (shrink)

Taxonomy Based modeling was applied to describe drivers’ mental models of variable message signs (VMS’s) displayed on expressways. Progress in road telematics has made it possible to introduce variable message signs (VMS’s). Sensors embedded in the carriageway every 500m record certain variables (speed, flow rate, etc.) that are transformed in real time into “driving times” to a given destination if road conditions do not change. VMS systems are auto-regulative Man-Machine (AMMI) systems which incorporate a model of the user: if (...) the traffic flow is too high, then drivers should choose alternative routes. In so doing, the traffic flow should decrease. The model of the user is based on suppositions such as: people do not like to waste time, they fully understand the displayed messages, they trust the displayed values, they know of alternative routes. However, people also have a model of the way the system functions. And if they do not believe the contents of the message, they will not act as expected. (shrink)

This book analyses the role of diagrammatic reasoning in Plato’s philosophy: the readers will realize that Plato, describing the stages of human cognitive development using a diagram, poses a logic problem to stimulate the general reasoning abilities of his readers. Following the examination of mental models in this book, the readers will reflect on what inferences can be useful to approach this kind of logic problem. Plato calls for a collaboration between writer and readers. In (...) this book the readers will examine the connection between diagrams and discovery, realizing the important epistemic role of visualization. They will recognize the crucial role that diagrams play in problem solving. The logic problem elaborated by Plato is addressed considering the epistemic function of mental models. These models introduce to an advanced stage of cognitive development, in which reasoning uses in its investigations a higher-level of mathematical complexity, represented by structuralism. (shrink)

A problem related to theWason selection task is that only some thematic versions of it are executed correctly. Fodor raises the thesis that the versions that are adequately solved are those that refer to deontic situations. In his opinion, there is a deontic logic that is different to classical logic and that allows reasoning appropriately in deontic contexts. In this paper, I review Fodor’s arguments, question his assumptions, and propose an alternative explanation, based on the mental (...) class='Hi'>models theory, of why only some versions of the selection task with thematic content offer optimal results. (shrink)

Divided-mind approaches to the conflict involved in self-control are pervasive. According to an influential version of the divided-mind approach, self-control conflict is a dispute between affective reactions and “cold” cognitive processes. I argue that divided-mind approaches are based on problematic bipartite architectural assumptions. Thus views that understand self-control as “control _of_ the self” might be better suited to account for self-control. I subsequently aim to expand on this kind of view. I suggest that self-control conflict involves a rivalry between narrative (...) self-models aimed at reducing error, analogous to model rivalry in binocular rivalry paradigms. This approach straightforwardly accounts for the sense of conflict that is characteristic of self-control within a unified-mind approach, and among its other explanatory advantages, it directly aligns with current views that account for addiction in terms of maladaptive self-representational processes. (shrink)

In this paper we analyze two recent conditional interpretations of defaults, one based on probabilities, and the other, on models. We study what makes them equivalent, explore their limitations and develop suitable extensions. The resulting framework ties together a number of important notions in default reasoning, like high-probabilities and model-preference, default priorities and argument systems, and independence assumptions and minimality considerations.

Judges and jurors must make decisions in an environment of ignoranceand uncertainty for example by hearing statements of possibly unreliable ordishonest witnesses, assessing possibly doubtful or irrelevantevidence, and enduring attempts by the opponents to manipulate thejudge''s and the jurors'' perceptions and feelings. Three importantaspects of decision making in this environment are the quantificationof sufficient proof, the weighing of pieces of evidence, and therelevancy of evidence. This paper proposes a mathematical frameworkfor dealing with the two first aspects, namely the quantification ofproof (...) and weighing of evidence. Our approach is based on subjectivelogic, which is an extension of standard logic and probability theory,in which the notion of probability is extended by including degrees ofuncertainty. Subjective Logic is a framework for modelling humanreasoning and we show how it can be applied to legalreasoning. (shrink)

This study investigated individual differences in the belief bias effect, which is the tendency to accept conclusions because they are believable rather than because they are logically valid. It was observed that the extent of an individual's belief bias effect was unrelated to a number of measures of reasoning competence. Instead, as predicted by mental models theory, it was related to a person's ability to generate alternative representations of premises: the more alternatives a person generated, the less likely (...) they were to show a belief bias effect. In contrast to belief effects, which were predicted by the number of alternatives generated, scores on logical reasoning tasks were predicted by an individual's understanding of the concept of logical necessity. These two mediating variables, ability to generate alternatives and understanding of logical necessity, were themselves predicted by similar variables, such as cognitive motivation and abstract reasoning ability. Our findings strongly support the mental models interpretation of the belief bias effect, and suggest that individual differences in this effect are associated with a specific ability to generate alternatives, rather than with a general logical competence. (shrink)

Logic, Argumentation & Reasoning explores the links between Humanities and the Social Sciences, with theories including, decision and action theory as well as cognitive sciences, economy, sociology, law, logic, and philosophy of sciences. It’s two main ambitions are to develop a theoretical framework that will encourage and enable interaction between disciplines as well as to federate the Humanities and Social Sciences around their main contributions to public life: using informed debate, lucid decision-making and action based on reflection. (...) The series welcomes research from the analytic and continental traditions, putting emphasis on four main focus areas: • Argumentation models and studies • Communication, language and techniques of argumentation • Reception of arguments, persuasion and the impact of power • Diachronic transformations of argumentative practices The Series is developed in partnership with the Maison Européenne des Sciences de l’Homme et de la Société (MESHS) at Nord - Pas de Calais and the UMR-STL: 8163 (CNRS). Proposals should include : • A short synopsis of the work or the introduction chapter • The proposed Table of Contents • The CV of the lead author(s) • If available: one sample chapter We aim to make a first decision within 1 month of submission. In case of a positive first decision the work will be provisionally contracted: the final decision about publication will depend upon the result of the anonymous peer review of the complete manuscript. We aim to have the complete work peer-reviewed within 3 months of submission. The series discourages the submission of manuscripts that contain reprints of previous published material and/or manuscripts that are below 150 pages / 85,000 words. (shrink)

We consider systems of rational agents who act and interact in pursuit of their individual and collective objectives. We study and formalise the reasoning of an agent, or of an external observer, about the expected choices of action of the other agents based on their objectives, in order to assess the reasoner’s ability, or expectation, to achieve their own objective. To formalize such reasoning we extend Pauly’s Coalition Logic with three new modal operators of conditional strategic (...) class='Hi'>reasoning, thus introducing the Logic for Local Conditional Strategic Reasoning \. We provide formal semantics for the new conditional strategic operators in concurrent game models, introduce the matching notion of bisimulation for each of them, prove bisimulation invariance and Hennessy–Milner property for each of them, and discuss and compare briefly their expressiveness. Finally, we also propose systems of axioms for each of the basic operators of \ and for the full logic. (shrink)

In this paper we present two families of probability logics (denoted _QLP_ and $QLP^{ORT}$ ) suitable for reasoning about quantum observations. Assume that $\alpha$ means “O = a”. The notion of measuring of an observable _O_ can be expressed using formulas of the form $\square \lozenge \alpha$ which intuitively means “if we measure _O_ we obtain $\alpha$ ”. In that way, instead of non-distributive structures (i.e., non-distributive lattices), it is possible to relay on classical logic (...) extended with the corresponding modal laws for the modal logic ${\textbf{B}}$. We consider probability formulas of the form $CS_{z_{1},\rho _{1}; \ldots ; z_{m},\rho _{m}} \square \lozenge \alpha$ related to an observable _O_ and a possible world (vector) _w_: if _a_ is an eigenvalue of _O_, $w_{1}$,..., $w_{m}$ form a base of a closed subspace of the considered Hilbert space which corresponds to eigenvalue _a_, and if _w_ is a linear combination of the basis vectors such that $w=c_{1}\cdot w_{1}+ \cdots + c_{m}\cdot w_{m}$ for some $c_{i}\in {\mathbb {C}}$, then $\Vert c_{1}-z_{1}\Vert \le \rho _{1}$,..., $\Vert c_{m}-z_{m}\Vert \le \rho _{m}$, and the probability of obtaining _a_ while measuring _O_ in the state _w_ is equal to $\Sigma _{i=1}^{m}\Vert c_{i}\Vert ^{2}$. Formulas are interpreted in reflexive and symmetric Kripke models equipped with probability distributions over families of subsets of possible worlds that are orthocomplemented lattices, while for $QLP^{ORT}$ also satisfy ortomodularity. We give infinitary axiomatizations, prove the corresponding soundness and strong completeness theorems, and also decidability for _QLP_-logics. (shrink)

Cognitive psychology investigates the structural properties of human reasoning. We review some achievements of this kind of research and give a critical evaluation of its methods.

Reasoning with conditionals is often thought to be non-monotonic, but there is no incompatibility with classical logic, and no need to formalise inference itself as probabilistic. When the addition of a new premise leads to abandonment of a previously compelling conclusion reached by modus ponens, for example, this is generally because it is hard to think of a model in which the conditional and the new premise are true.

Around 1950, B.A. Trakhtenbrot proved an important undecidability result (known, by a pure accident, as \Trakhtenbrot's theorem"): there is no algorithm to decide, given a rst-order sentence, whether the sentence is satis able in some nite model. The result is in fact true even if we restrict ourselves to languages that has only one binary relation Tra63]. It is hardly conceivable that at that time Prof. Trakhtenbrot expected his result to in uence the development of the theory of relational databases (...) query languages, but it did. This perhaps is not surprising in view of the following two facts: 1) The theory of relational databases is strongly rooted in logic and can easily be abstracted to make it a branch of mathematical logic. 2) The main interest in the theory of relational databases is in nite relations. In the rst section we explain those two points in more detail. Then, in section 2 of the present paper, we discuss the question: \What constitutes a reasonable query to a database?" The discussion naturally leads to a certain class of queries, known as the \domain independent" queries, as an ideal query language. At this point Trakhtenbrot's theorem appears as a major obstacle, since it easily implies that this ideal class is undecidable. Real query languages cannot be allowed to have this property. Section 3 outlines then several possible ways to circumvent this di culty. The following section explains the.. (shrink)

Taxonomy Based modeling was applied to describe drivers' mental models of variable message signs (VMS's) displayed on expressways. Progress in road telematics has made it possible to introduce variable message signs (VMS's). Sensors embedded in the carriageway every 500m record certain variables (speed, flow rate, etc.) that are transformed in real time into 'driving times' to a given destination if road conditions do not change. VMS systems are auto-regulative Man-Machine (AMMI) systems which incorporate a model of the user: if (...) the traffic flow is too high, then drivers should choose alternative routes. In so doing, the traffic flow should decrease. The model of the user is based on suppositions such as: people do not like to waste time, they fully understand the displayed messages, they trust the displayed values, they know of alternative routes. However, people also have a model of the way the system functions. And if they do not believe the contents of the message, they will not act as expected. We collected data through interviews with drivers using the critical incidents technique (Flanagan, 1985). Results show that the mental models that drivers have of the way the VMS system works are various but not numerous and that most of them differ from the 'ideal expert' mental model. It is clear that users don't have an adequate model of how the VMS system works and that VMS planners have a model of user behaviour that does not correspond to the behaviour of the drivers we interviewed. Finally, Taxonomy Based Modeling is discussed as a tool for mental model remediation. (shrink)

Counterfactual reasoning has been used to account for many aspects of scientific reasoning. More recently, it has also been used to account for the scientific practice of modeling. Truth in a model is truth in a situation considered as counterfactual. When we reason with models, we reason with counterfactuals. Focusing on selected models like Bohr’s atom model or models of population dynamics, I present an account of how the imaginative development of a counterfactual supposition leads (...) us from reality to interesting model assumptions; how it guides our reasoning from these assumptions to interesting consequences for the model scenario via counterfactual entailment; and how it leads us back to conclusions on real target phenomena. (shrink)

The study of some real reasonings (observed in the Humanities) reveals the very heterogeneous nature of the arguments used in the building of scientific knowledge and the complexity of their overall architecture. The building of a formal theory of the trace of these mental processes on the classical grounds of logic seems quite impossible. Instead, we propose a flexible methodology based on some local formal models, integrated in a global strategy. This strategy allows an empirical, but systematic, description (...) of the process of reasoning as a whole.The local models can be very different, from plausible inference to conditional transitivity. Their integration is based on some argumentative markers or structures (topoï). We propose a procedural semantics for some of them.This paper is based on the AVEROES Project, a study of the sea-borne trade in the Occidental Mediterranean Sea during the Roman Empire. (shrink)

Sieg has proposed axioms for computability whose models can be reduced to Turing machines. This lecture will investigate to what extent these axioms hold for reasoning. In particular we focus on the requirement that the configurations that a computing agent (whether human or machine) operates on must be ’immediately recognisable’. If one thinks of reasoning as derivation in a calculus, this requirement is satisfied; but even in contexts which are only slightly less formal, the requirement cannot be (...) met. Our main example will be the Wason selection task, a propositional reasoning task in which in a typical (undergraduate) subject group only around 5% arrive at the answer dictated by classical logic. The instructions for this task (as well as other standard tasks in the psychology of reasoning, such as syllogisms) do not contain any ’immediately recognisable’ configurations. The subject must try to find an interpretation of the task by making the various elements in the instructions cohere, in effect solving a difficult constraint satisfaction problem, which has no unique solution. The subject has given a complete interpretation of the task if she can formulate the problem posed in the task as a theorem to be proved. The complexity of such theorems can be quite high; e.g. for the propositional Wason selection task the theorem can be in Σ1 3 . This sounds implausible, but we’ll present experimental data confirming this point. (shrink)

In the paper, we study the dynamics of coalitional ability by proposing an extension of coalition logic (CL). CL allows one to reason about what a coalition of agents is able to achieve through a joint action, no matter what agents outside of the coalition do. The proposed dynamic extension is inspired by dynamic epistemic logic, and, in particular, by action models. We call the resulting logic coalition action model logic (CAML), which, compared to CL, (...) includes additional modalities for coalitional action models. We investigate the expressivity of CAML, and provide a complexity characterisation of its model checking problem. (shrink)

This chapter provides broad coverage of the notion of logical consequence, exploring its modal, semantic, and epistemic aspects. It develops the contrast between proof-theoretic notion of consequence, in terms of deduction, and a model-theoretic approach, in terms of truth-conditions. The main purpose is to relate the formal, technical work in logic to the philosophical concepts that underlie reasoning.

We develop a logical modelling approach to describe evolvable computational systems. In this account, evolvable systems are built hierarchically from components where each component may have an associated supervisory process. The supervisor's purpose is to monitor and possibly change its associated component. Evolutionary change may be determined purely internally from observations made by the supervisor or may be in response to external change. Supervisory processes may be present at any level in the component hierarchy allowing us to use evolutionary behaviour (...) as an integral part of system design. We model such systems in a revision-based first-order logical framework in which supervisors are modelled as theories which are at a logical meta-level to the theories of their components. This enables evolutionary change of the component to be induced by revision-based changes of the supervisor at the meta-level. In this way, the intervention required in evolutionary change is modelled purely logically. The hierarchical component-based structure is fairly intricate so we present the basic ideas firstly in a simple setting, the well-known blocks world, before introducing tree-based structures to represent component hierarchies. We also introduce some techniques for establishing the behaviour of evolvable systems specified in this logical framework. The ideas and concepts are driven by example throughout. We conclude with a more substantial example, that of a simple model of an evolvable system of automated bank teller machines. (shrink)

This paper argues that chance (risk or opportunity) discovery is challenging, from a reasoning point of view, because it represents a dilemma for inductive reasoning. Chance discovery shares many features with the grue paradox. Consequently, Bayesian approaches represent a potential solution. The Bayesian solution evaluates alternative models generated using a temporal logic planner to manage the chance. Surprise indices are used in monitoring the conformity of the real world and the assessed probabilities. Game theoretic approaches are (...) proposed to deal with multi-agent interaction in chance management. (shrink)

We interpret the modal µ-calculus over a new model [10], to give a temporal logic suitable for systems exhibiting both probabilistic and demonic nondeterminism. The logical formulae are real-valued, and the statements are not limited to properties that hold with probability 1. In achieving that conceptual step, our technical contribution is to determine the correct quantitative generalisation of the Boolean operators: one that allows many of the standard Boolean-based temporal laws to carry over the reals with little or no (...) structural alteration, even for properties that hold with probability strictly between 0 and 1. The generalisation is not obvious, but is dictated by our discovery elsewhere of the algebraic property that characterises the next-time operator over the new model: it is arithmetic 'sublinearity' [20, Fig. 4 p. 342], which replaces the Boolean conjunctivity that characterises next-time in a modal algebra.We confirm by example that the new modal laws can be used for quantitative reasoning about probabilistic/demonic behavior. The random walk is treated using only those laws and real-number arithmetic: arguing from precise numeric premises, more specific than simply 'with some non-zero probability', we reach numeric conclusions that are not simply 'with probability 1'. (shrink)

This paper briefly outlines some advancements in paraconsistent logics for modelling knowledge representation and reasoning. Emphasis is given on the so-called Logics of Formal Inconsistency (LFIs), a class of paraconsistent logics that formally internalize the very concept(s) of consistency and inconsistency. A couple of specialized systems based on the LFIs will be reviewed, including belief revision and probabilistic reasoning. Potential applications of those systems in the AI area of KRR are tackled by illustrating some examples that emphasizes the (...) importance of a fine-tuned treatment of consistency in modelling reputation systems, preferences, argumentation, and evidence. (shrink)

We offer an alternative approach to the existing methods for intuitionistic formalization of reasoning about probability. In terms of Kripke models, each possible world is equipped with a structure of the form $\langle H, \mu \rangle$ that needs not be a probability space. More precisely, though _H_ needs not be a Boolean algebra, the corresponding monotone function (we call it measure) $\mu : H \longrightarrow [0,1]_{\mathbb {Q}}$ satisfies the following condition: if $\alpha$, $\beta$, \(\alpha \wedge (...) \beta \), $\alpha \vee \beta \in H$, then $\mu (\alpha \vee \beta ) = \mu (\alpha ) + \mu (\beta ) - \mu (\alpha \wedge \beta )$. Since the range of $\mu$ is the set $[0,1]_{\mathbb {Q}}$ of rational numbers from the real unit interval, our logic is not compact. In order to obtain a strong complete axiomatization, we introduce an infinitary inference rule with a countable set of premises. The main technical results are the proofs of strong completeness and decidability. (shrink)