Probabilistic Relational Models (PRMs) are a framework for compactly representing uncertainties (actually probabilities). They result from the combination of Bayesian Networks (BNs), Object-Oriented languages, and relational models. They are specifically designed for their efficient construction, maintenance and exploitation for very large scale problems, where BNs are known to perform poorly. Actually, in large-scale problems, it is often the case that BNs result from the combination of patterns (small BN fragments) repeated many times. PRMs exploit this feature by defining these patterns (...) only once (the so-called PRM’s classes) and using them through multiple instances, as prescribed by the Object-Oriented paradigm. This design induces low construction and maintenance costs. In addition, by exploiting the classes’ structures, PRM’s state-of-the-art inference algorithm “Structured Variable Elimination” (SVE) significantly outperforms BN’s classical inference algorithms (e.g., Variable Elimination, VE; Local Conditioning, LC). SVE is actually an extension of VE that simply exploits classes to avoid redundant computations. In this article, we show that SVE can be enhanced using LC. Although LC is often thought as being outperformed by VE-like algorithms in BNs, we do think that it should play an important role for PRMs because its features are very well suited for best exploiting PRM classes. In this article, relying on Faÿ and Jaffray’s works, we show how LC can be used in conjunction with VE and deduce an extension of SVE that outperforms it for large-scale problems. Numerical experiments highlight the practical efficiency of our algorithm. (shrink)

Prior to the twentieth century, theories of knowledge were inherently perceptual. Since then, developments in logic, statis- tics, and programming languages have inspired amodal theories that rest on principles fundamentally different from those underlying perception. In addition, perceptual approaches have become widely viewed as untenable because they are assumed to implement record- ing systems, not conceptual systems. A perceptual theory of knowledge is developed here in the context of current cognitive science and neuroscience. During perceptual experience, association areas in the (...) brain capture bottom-up patterns of activation in sensory-motor areas. Later, in a top-down manner, association areas partially reactivate sensory-motor areas to implement perceptual symbols. The stor- age and reactivation of perceptual symbols operates at the level of perceptual components – not at the level of holistic perceptual expe- riences. Through the use of selective attention, schematic representations of perceptual components are extracted from experience and stored in memory (e.g., individual memories of green, purr, hot). As memories of the same component become organized around a com- mon frame, they implement a simulator that produces limitless simulations of the component (e.g., simulations of purr). Not only do such simulators develop for aspects of sensory experience, they also develop for aspects of proprioception (e.g., lift, run) and introspec- tion (e.g., compare, memory, happy, hungry). Once established, these simulators implement a basic conceptual system that represents types, supports categorization, and produces categorical inferences. These simulators further support productivity, propositions, and ab- stract concepts, thereby implementing a fully functional conceptual system. Productivity results from integrating simulators combinato- rially and recursively to produce complex simulations. Propositions result from binding simulators to perceived individuals to represent type-token relations. Abstract concepts are grounded in complex simulations of combined physical and introspective events. Thus, a per- ceptual theory of knowledge can implement a fully functional conceptual system while avoiding problems associated with amodal sym- bol systems. Implications for cognition, neuroscience, evolution, development, and artificial intelligence are explored. (shrink)

No False Lemmas (NFL) says: necessarily, S’s belief that p is knowledge only if it is not inferred from any falsehood. Its proponents argue that alleged counterexamples to NFL are really cases of knowledge despite falsehood, wherein the false premise is inessential to the inference; perhaps some nearby truth does the justificatory heavy-lifting. We argue that there can be cases of inferential knowledge from a blindspot premise. Given that in such cases the relevant falsehood is essential to the (...) class='Hi'>inference, one cannot employ the knowledge despite falsehood strategy to defend NFL. We conclude by discussing how cases of knowledge from blindspots exemplify one way in which we can gain inferential knowledge defectively or non-ideally. (shrink)

These notes discuss formalizing contexts as first class objects. The basic relationships are: ist(c,p) meaning that the proposition p is true in the context c, and value(c,p) designating the value of the term e in the context c Besides these, there are lifting formulas that relate the propositions and terms in subcontexts to possibly more general propositions and terms in the outer context. Subcontextx are often specialised with regard to time, place and terminology. Introducing contexts as formal objects will permit (...) axiomatizations in limited contexts to be expanded to transcend the original limitations. This seems necessary to provide AI programs using logic with certain capabilities that human fact representation and human reasoning possess. Fully implementing transcendence seems to require further extensions to mathematical logic, ie. beyond the nonmonotonic inference methods first invented in AI and now studied as a new domain of logic. (shrink)

Infants can see someone pointing to one of two buckets and infer that the toy they are seeking is hidden inside. Great apes do not succeed in this task, but, surprisingly, domestic dogs do. However, whether children and dogs understand these communicative acts in the same way is not yet known. To test this possibility, an experimenter did not point, look, or extend any part of her body towards either bucket, but instead lifted and shook one via a centrally (...) pulled rope. She did this either intentionally or accidentally, and did or did not address her act to the subject using ostensive cues. Young 2-year-old children but not dogs understood the experimenter’s act in intentional conditions. While ostensive pulling of the rope made no difference to children’s success, it actually hindered dogs’ performance. We conclude that while human children may be capable of inferring communicative intent from a wide variety actions, so long as these actions are performed intentionally, dogs are likely to be less flexible in this respect. Their understanding of communicative intention may be more dependent upon bodily markers of communicative intent, including gaze, orientation, extended limbs, and vocalisations. This may be because humans have come under selective pressure to develop skills for communicating with absent interlocutors – where bodily co-presence is not possible. (shrink)

Inspired by the supervenience-determined consequence relation and the semantics of agreement operator, we introduce a modal logic of supervenience, which has a dyadic operator of supervenience as a sole modality. The semantics of supervenience modality very naturally correspond to the supervenience-determined consequence relation, in a quite similar way that the strict implication corresponds to the inference-determined consequence relation. We show that this new logic is more expressive than the modal logic of agreement, by proposing a notion of bisimulation for (...) the latter. We provide a sound proof system for the new logic. We lift onto more general logics of supervenience. Related to this, we address an interesting open research direction listed in the literature, by comparing propositional logic of determinacy and noncontingency logic in expressive powers and axiomatizing propositional logic of determinacy over various classes of frames. We also obtain an alternative axiomatization for propositional logic of determinacy over universal models. (shrink)

The problem of psychologism in the philosophy of logic and the different solutions of this problem are considered. Both traditional psychologistic and antipsychologistic solutions are shown to be untenable and the need for a new solution is demonstrated. The original program of metapsychologism is advanced as a solution to the problem of psychologism based on deduction-search theory. Two formalized levels of a logical procedure are distinguished: 1) an object-level at which a notion of inference is formalized; 2) a metalevel (...) at which principles of deduction-search are formalized, and a thesis of metapsychologism according to which metalevel processes are formulated. Metapsychologism lifts usual psychologist considerations one level up in the hierarchy of logical procedure, while a nonpsychologist justification of logical relations is kept at the object-level. The application of the thesis of metapsychologism to different concrete logical procedures is considered. (shrink)

THE ART OF CAUSAL CONJECTURE Glenn Shafer Table of Contents Chapter 1. Introduction........................................................................................ ...........1 1.1. Probability Trees..........................................................................................3 1.2. Many Observers, Many Stances, Many Natures..........................................8 1.3. Causal Relations as Relations in Nature’s Tree...........................................9 1.4. Evidence............................................................................................ ...........13 1.5. Measuring the Average Effect of a Cause....................................................17 1.6. Causal Diagrams..........................................................................................20 1.7. Humean Events............................................................................................23 1.8. Three Levels of Causal Language................................................................27 1.9. An Outline of the Book................................................................................27 Chapter 2. Event Trees............................................................................................... .....31 2.1. Situations and Events...................................................................................32 2.2. The Ordering of Situations and Moivrean Events.......................................35 2.3. Cuts................................................................................................ ..............39 2.4. Humean Events............................................................................................43 2.5. (...) Moivrean Variables......................................................................................49 2.6. Humean Variables........................................................................................53 2.7. Event Trees for Stochastic Processes...........................................................54 2.8. Timing in Event Trees.................................................................................56 2.9. Intersecting Event Trees...............................................................................60 2.10. Notes on the Literature...............................................................................61 Chapter 3. Probability Trees...........................................................................................63 3.1. Some Types of Probability Trees.................................................................64 ii 3.2. Axioms for the Probabilities of Moivrean Events.......................................68 3.3. Zero Probabilities....................................................................................... ..70 3.4. A Sample-Space Analysis of the Event-Tree Axioms.................................72 3.5. Probabilities and Expected Values for Variables.........................................74 3.6. Martingales......................................................................................... .........79 3.7. The Expectation of a Variable in a Cut........................................................83 3.8. Conditional Expected Value and Conditional Expectation.........................87 Chapter 4. The Meaning of Probability...........................................................................91 4.1. The Interpretation of Expected Value..........................................................92 4.2. The Interpretation of Expectation................................................................95 4.3. The Long Run..............................................................................................98 4.4. Changes in Belief.........................................................................................101 4.5. The Empirical Validation of Probability......................................................106 4.6. The Diversity of Uses of Probability...........................................................108 4.7. Notes on the Literature.................................................................................110 Chapter 5. Independent Events.......................................................................................113 5.1. Independence........................................................................................ .......114 5.2. Weak Independence.....................................................................................118 5.3. The Principle of the Common Cause...........................................................121 5.4. Conditional Independence............................................................................128 5.5. Notes on the Literature.................................................................................133 Chapter 6. Events Tracking Events.................................................................................135 6.1. Tracking............................................................................................ ...........137 6.2. Tracking and Conditional Independence.....................................................142 6.3. Stochastic Subsequence...............................................................................143 6.4. Singular Diagrams for Stochastic Subsequence...........................................147 6.5. Conjunctive and Interactive Forks...............................................................149 Chapter 7. Events as Signs of Events..............................................................................153 iii 7.1. Sign................................................................................................ ..............154 7.2. Weak Sign................................................................................................ ....159 7.3. The Ethics of Causal Talk............................................................................160 7.4. Screening Off...............................................................................................16 2 Chapter 8. Independent Variables...................................................................................167 8.1. Unconditional Independence........................................................................170 8.2. Conditional Independence............................................................................175 8.3. Independence for Partitions.........................................................................177 8.4. Independence for Families of Variables......................................................182 8.5. Individual Properties of the Independence Relations...................................186 Chapter 9. Variables Tracking Variables........................................................................189 9.1. Tracking and Conditional Independence: A Summary...............................190 9.2. Strong Tracking............................................................................................ 192 9.3. Strong Tracking and Conditional Independence..........................................198 9.4. Stochastic Subsequence...............................................................................201 9.5. Functional Dependence................................................................................203 9.6. Tracking in Mean.........................................................................................204 9.7. Linear Tracking............................................................................................ 207 9.8. Tracking by Partitions..................................................................................210 9.9. Tracking by Families of Variables...............................................................212 Chapter 10. Variables as Signs of Variables...................................................................215 10.1. Sign................................................................................................ ............219 10.2. Linear Sign................................................................................................ .222 10.3. Scored Sign................................................................................................ 225 10.4. Families of Variables.................................................................................227 Chapter 11. AnTheory of Event Trees.............................................................229 11.1. Event Trees as Sets of Sets........................................................................230 11.2. Event Trees as Partially Ordered Sets........................................................232 iv 11.3. Regular Event Trees...................................................................................240 11.4. The Resolution of Moivrean Variables......................................................244 11.5. Humean Events and Variables...................................................................246 Chapter 12. Martingale Trees..........................................................................................247 12.1. Examples of Decision Trees......................................................................249 12.2. The Meaning of Probability in a Decision Tree.........................................253 12.3. Martingales......................................................................................... .......257 12.4. The Structure of Martingale Trees.............................................................261 12.5. Probability and Causality...........................................................................265 12.6. Lower and Upper Probability.....................................................................269 12.7. The Law of Large Numbers.......................................................................272 12.8. Notes on the Literature...............................................................................274 Chapter 13. Refining............................................................................................ ...........275 13.1. Examples of Refinement............................................................................277 13.2. A Constructive Definition of Finite Refinement.......................................281 13.3. Axioms for Refinement..............................................................................282 13.4. Lifting Moivrean Events and Variables.....................................................288 13.5. Refining Martingale Trees.........................................................................288 13.6. Grounding........................................................................................... .......294 Chapter 14. Principles of Causal Conjecture..................................................................299 14.1. The Diversity of Causal Explanation.........................................................302 14.2. The Mean Effect of the Happening of a Moivrean Event..........................305 14.3. The Effect of a Humean Variable..............................................................311 14.4. Attribution and Generality.........................................................................316 14.5. The Statistical Measurement of the Effect of a Cause...............................319 14.6. Measurement by Experiment.....................................................................320 14.7. Using Our Knowledge of How Things Work............................................322 v 14.8. Sampling Error...........................................................................................329 14.9. The Sampling Frame..................................................................................329 14.10. Notes on the Literature.............................................................................330 Chapter 15. Causal Models.............................................................................................3 31 15.1. The Causal Interpretation of Statistical Prediction....................................333 15.2. Generalizing to a Family of Exogenous Variables....................................337 15.3 Some Joint Causal Diagrams......................................................................339 15.4. Causal Path Diagrams................................................................................342 15.5. Causal Relevance Diagrams.......................................................................346 15.6. The Meaning of Latent Variables..............................................................352 15.7. Notes on the Literature...............................................................................357 Chapter 16. Representing Probability Trees...................................................................359 16.1. Three Graphical Representations...............................................................361 16.2. Skeletal Simplifications.............................................................................368 16.3. Martingale Trees in Type Theory...............................................................371 Appendix A. Huygens’s Probability Trees.....................................................................379 Huygens’s Manuscript in Translation..................................................................380 Appendix B. Some Elements of Graph Theory..............................................................385 B1. Undirected Graphs........................................................................................385 B2. Directed Graphs............................................................................................38 6 Appendix C. Some Elements of Order Theory...............................................................393 C1. Partial and Quasi Orderings.........................................................................393 C2. Singular and Joint Diagrams for Binary Relations.......................................394 C3. Lattices............................................................................................ .............395 C4. The Lattice of Partitions of a Set..................................................................396 Appendix D. The Sample-Space Framework for Probability.........................................399 D1. Probability Measures....................................................................................399 D2. Variables........................................................................................... ...........400 vi D3. Families of Variables...................................................................................401 D4. Expected Value............................................................................................402 D5. The Law of Large Numbers.........................................................................405 D6. Conditional Probability................................................................................406 D7. Conditional Expected Value........................................................................407 Appendix E. Prediction in Probability Spaces................................................................409 E1. Conditional Distribution...............................................................................411 E2. Regression on a Single Variable...................................................................412 E3. Regression on a Partition or a Family of Variables......................................415 E4. Linear Regression on a Single Variable.......................................................418 E5. Linear Regression on a Family of Variables................................................422 Appendix F. Sample-Space Concepts of Independence.................................................425 F1. Overview............................................................................................ ...........426 F2. Independence Proper.....................................................................................432 F3. Unpredictability in Mean..............................................................................434 F4. Simple Uncorrelatedness..............................................................................437 F5. Mixed Uncorrelatedness...............................................................................438 F6. Partial Uncorrelatedness...............................................................................440 F7. Independence for Partitions..........................................................................442 F8. Independence for Families of Variables.......................................................445 F9. The Basic Role of Uncorrelatedness.............................................................448 F10. Dawid’s Axioms.........................................................................................449 Appendix G. Prediction Diagrams..................................................................................453 G1. Path Diagrams............................................................................................ ..454 G2. Generalized Path Diagrams..........................................................................462 G3. Relevance Diagrams.....................................................................................466 G4. Bubbled Relevance Diagrams......................................................................475 Appendix H. Abstract Stochastic Processes...................................................................479 vii H1. Probability Conditionals and Probability Distributions...............................477 H2. Abstract Stochastic Processes......................................................................479 H3. Embedding Variables and Processes in a Sample Space.............................480 References.......................................................................................... ..............................491. (shrink)

This dissertation is intended to provide a formalism for those generics that trigger nonmonotonic inferences. The formalism is to reflect intentionality and exception-tolerating features of generics, and has an emphasis on the axiomatization of generic reasoning that encodes nonmonotonicity. ;A modal conditional approach is taken to formalize the nonmonotonic reasoning in general at the level of object language. A serial of logic systems---MN, NID, NCUM, N STCUM---are constructed in an increasing strength of the characterized nonmonotonic inference relation. In these (...) systems, two binary modal operators ⩾ and > are introduced in their syntax, and a ⊛ function lifted from the traditional * function is deployed in their semantics. These systems are shown to be sound and complete with respect to certain classes of frames defined in the semantics. They are decidable as well. The nonmonotonic inference is argued to be a ternary relation "[phi], Gamma |∼ alpha", and is defined in the system NSTCUM. Many widely discussed nonmonotonic inference patterns such as Defeasible Modus Ponens, Defeasible Transitivity, the Penguin Principle etc. are justified. The specificity rule is proved to be a theorem of the system N STCUM. The impact of negated defaults on an inference is also investigated and accounted for. ;A canonical form to read off generics is proposed: All generic sentences with subject-predicate structure can be re-written into their canonical form S . If S is a plural noun phrase, it can be further refined to be . Normal objects are selected based on the "meaning" of the subject and predicate terms. The second parameter provides an aspect with respect to which certain objects of a kind are considered normal. Due to such a way to select normal objects, the drowning problem is solved. ;The inference behaviors of generics are axiomatized in the system G, which is a quantificational extension of the system NSTCUM. It is proved to be sound and complete with respect to the class of L⩾,G -frames. Those benchmark examples of generic inferences are examined in the system G. (shrink)

In this paper, we axiomatize the deontic logic in Fusco (2015), which uses a Stalnaker-inspired account of diagonal acceptance and a two-dimensional account of disjunction to treat Ross’s Paradox and the Puzzle of Free Choice Permission. On this account, disjunction-involving validities are a priori rather than necessary. We show how to axiomatize two-dimensional disjunction so that the introduction/elimination rules for boolean disjunction can be viewed as one-dimensional projections of more general two-dimensional rules. These completeness results help make explicit the restrictions (...) Fusco’s account must place on free-choice inferences. They are also of independent interest, as they raise difficult questions about how to “lift” a Kripke frame for a one-dimensional modal logic into two dimensions. (shrink)

One of the fundamental properties inclassical equational reasoning isLeibniz's principle of substitution. Unfortunately, this propertydoes not hold instandard epistemic logic. Furthermore,Herbrand's lifting theorem which isessential to thecompleteness ofresolution andParamodulation in theclassical first order logic (FOL), turns out to be invalid in standard epistemic logic. In particular, unlike classical logic, there is no skolemization normal form for standard epistemic logic. To solve these problems, we introduce anintensional epistemic logic, based on avariation of Kripke's possible-worlds semantics that need not have a constant (...) domain. We show how a weaker notion of substitution through indexed terms can retain the Herbrand theorem. We prove how the logic can yield a satisfibility preserving skolemization form. In particular, we present an intensional principle for unifing indexed terms. Finally, we describe asound andcomplete inference system for a Horn subset of the logic withequality, based onepistemic SLD-resolution. (shrink)

I argue that idealization can throw a new light upon Freud’s theory of sublimation and that courtly love can be seen as an illustration of this suggestion. For Freud sublimation is the process in which the sexual aim of the instincts is diverted towards a non-sexual aim that is still related with the original one. Freud’s theory struggles with at least two problems.The first problem regards the relation between the terminus a quo and the terminus ad quem. Freud describes this (...) relation with different terms. The notion of ‘desexualization’ represents precisely what he has in mind. This term propounds that Freud understands sublimation as a one-sided movement that consists in leaving behind the original sexual aim. Courtly love proves that desexualization, as Freud understands it, is not a necessary condition for sublimation. A weakening of Freud’s strong claim concerning desexualization implies however that the distinction between sublimation and perversion is not always clearcut.The second problem appertains to the processes that bring about the transformation of the sexual aim. Courtly love infers that idealization of the love-object can play an important role in bringing about sublimation. The kind of sublimation that corresponds to courtly love is what has been called Verführung in German Idealism.Psychoanalytic theory is not willing to conceive idealization in this sense. According to the classical psychoanalytic theory, idealization produces repression of sexual instincts. I argue that this idea is counter-intuitive and that Freud’s understanding of idealization is more subtle. I give a short overview of Freud’s approach and I draw attention to some elements in his approach that help us to describe the direct link between idealization and sublimation.Idealization of the beloved can go together with an inhibition of sexual instincts. But it is wrong to identify aim-inhibition with repression or with a softening of the instincts. My suggestion is that the interaction between idealization and sublimation can be characterised as an interaction between an intensification of the sexual instincts, as it happens in any form of falling in love, and an inhibition of them.This interaction results in being lifted up above the sexual instincts that are caused by the idealised object. In religion and art, the double movement of the instincts is called ‘exaltation.’. (shrink)

This study investigates interpretations of the Japanese initial mora-based minimizer “X.Y...”-_no_ “X”-_no ji-mo_ ‘lit. even the letter “X” of “X.Y...”.’ Although initial mora-based minimizers have a literal interpretation of _ji_ ‘letter’, they have a non-literal interpretation as well. The non-literal interpretation has several distinctive features that are not present in ordinary minimizers. First, it is highly productive in that various expressions can appear in the form “X.Y...”-_no_ “X”-_no ji_. Second, non-literal minimizers typically co-occur with predicates that relate to knowledge, information, (...) concepts, thought, and habituality, as seen in the corpus data (Balanced Corpus of Contemporary Written Japanese [BCCWJ]). I argue that in the non-literal use, X refers to the minimum on the scale of the main predicate concerning “X.Y...”. I suggest that the non-literal use was developed as a result of the conventionalization of the pragmatic inference derived from the literal reading, and that the co-occurrence with predicates related to knowledge, information, knowledge, concepts, thought, or habituality is due to the interpretation of “X.Y...”, which were originally interpreted as letters as an abstract concept. The theoretical implication of this study is that, in addition to a non-compositional (lexically specified) minimizer whose scale is lexically fixed (e.g., _give a damn_, _lift a finger_), there also exists a compositional (lexically unspecified) minimizer in natural language, whose scale is specified via the predicate with which the minimizer co-occurs. The last section of this paper briefly discusses similar/related phenomena in Bosnian/Croatian/Serbian, Korean, and English from a cross-linguistic perspective. (shrink)

Technical reasoning refers to making inferences about how to use tools. The degree of technical reasoning is indicated by the bias of the gaze on the functional part of the tool when in use. Few studies have examined whether technical reasoning differs between familiar and unfamiliar novel tools. In addition, what effect the intention to use the tool has on technical reasoning has not been determined. This study examined gaze shifts in relation to familiar or unfamiliar tools, under three conditions, (...) among 14 healthy adults. The cumulative fixation time on the functional part of the tool served as a quantitative indicator of the degree of technical reasoning. The two-way analysis of variance for tools and conditions revealed that the cumulative fixation time significantly increased under free viewing and use conditions, compared to lift conditions. Relative to the free viewing condition, cumulative fixation time for unfamiliar tools significantly decreased in the lift condition and significantly increased in the use condition. Importantly, the results showed that technical reasoning was performed in both the use and the free viewing conditions. However, technical reasoning in the free viewing condition was not as strong as in the use condition. The difference between technical reasoning in free viewing and use conditions may indicate the difference between automatic and intentional technical reasoning. (shrink)

We can regard operations that discard information, like specializing to a particular case or dropping the intermediate steps of a proof, as projections, and operations that reconstruct information as liftings. By working with several projections in parallel we can make sense of statements like “Set is the archetypal Cartesian Closed Category”, which means that proofs about CCCs can be done in the “archetypal language” and then lifted to proofs in the general setting. The method works even when our archetypal (...) language is diagrammatical, has potential ambiguities, is not completely formalized, and does not have semantics for all terms. We illustrate the method with an example from hyperdoctrines and another from synthetic differential geometry. (shrink)

Inference versus consequence , an invited lecture at the LOGICA 1997 conference at Castle Liblice, was part of a series of articles for which I did research during a Stockholm sabbatical in the autumn of 1995. The article seems to have been fairly effective in getting its point across and addresses a topic highly germane to the Uppsala workshop. Owing to its appearance in the LOGICA Yearbook 1997 , Filosofia Publishers, Prague, 1998, it has been rather inaccessible. Accordingly it (...) is republished here with only bibliographical changes and an afterword. (shrink)

"How do we go about weighing evidence, testing hypotheses and making inferences? According to the model of 'inference to the Best explanation', we work out what to inter from the evidence by thinking about what would actually explain that evidence, and we take the ability of a hypothesis to explain the evidence as a sign that the hypothesis is correct. In inference to the Best Explanation, Peter Lipton gives this important and influential idea the development and assessment it (...) deserves." "The second edition has been substantially enlarged and reworked, with a new chapter on the relationship between explanation and Bayesianism, and an extension and defence of the account of contractive explanation. It also includes an expanded defence of the claims that our inferences really are guided by diverse explanatory considerations, and that this pattern of inference can take us towards the truth. This edition of Inference to the Best Explanation has also been updated throughout and incudes a new bibliography."--BOOK JACKET. (shrink)

In informal terms, abductive reasoning involves inferring the best or most plausible explanation from a given set of facts or data. It is a common occurrence in everyday life and crops up in such diverse places as medical diagnosis, scientific theory formation, accident investigation, language understanding, and jury deliberation. In recent years, it has become a popular and fruitful topic in artificial intelligence research. This volume breaks new ground in the scientific, philosophical, and technological study of abduction. It presents new (...) ideas about inferential and information-processing foundations for knowledge and certainty. The authors argue that knowledge arises from experience by processes of abductive inference, in contrast to the view that it arises non-inferentially, or that deduction and inductive generalization are enough to account for knowledge. Much AI research is hypothetical, so the importance of this book is that it reports key discoveries about abduction that have been made as a result of designing, building, testing, and analyzing actual working knowledge-based systems for medical diagnosis and other abductive tasks. The book tells the story of six generations of increasingly sophisticated generic abduction machines, RED-1, RED-2, PEIRCE, MDX2, TIPS, QUAWDS, and the discovery of reasoning strategies that make it computationally feasible to form well-justified composite explanatory hypotheses, despite the threat of combinatorial explosion. The final chapter argues that perception is logically abductive and presents a layered-abduction computational model of perceptual information processing. This book will be of great interest to researchers in AI, cognitive science, and philosophy of science. (shrink)

Delusional beliefs have sometimes been considered as rational inferences from abnormal experiences. We explore this idea in more detail, making the following points. Firstly, the abnormalities of cognition which initially prompt the entertaining of a delusional belief are not always conscious and since we prefer to restrict the term “experience” to consciousness we refer to “abnormal data” rather than “abnormal experience”. Secondly, we argue that in relation to many delusions (we consider eight) one can clearly identify what the abnormal cognitive (...) data are which prompted the delusion and what the neuropsychological impairment is which is responsible for the occurrence of these data; but one can equally clearly point to cases where this impairments is present but delusion is not. So the impairment is not sufficient for delusion to occur. A second cognitive impairment, one which impairs the ability to evaluate beliefs, must also be present. Thirdly (and this is the main thrust of our chapter) we consider in detail what the nature of the inference is that leads from the abnormal data to the belief. This is not deductive inference and it is not inference by enumerative induction; it is abductive inference. We offer a Bayesian account of abductive inference and apply it to the explanation of delusional belief. (shrink)

The lifting of lockdown is a typical case of the tragedy of the commons, and as such should be regulated by public authority, instead of being left to the ethics and responsibility of single individuals. I would therefore argue that we should think about an intermediate phase between the lockdown and the opening of shops (which in the Italian case is the transition from the red zone to the orange zone): diversified access to commercial activities, on an hourly basis, for (...) different population groups. This can be achieved either by creating different opening hours for different commercial activities and offices, or by opening them all at the same time but introducing free entrance hours based on age groups of clients. Both solutions would imply an extension of business and office hours, contrary to what has happened in most countries, where an attempt has been made to shorten the days and in some cases, such as in Italy, a curfew has even been introduced at a certain time of the day (in Italy, at 10 pm). (shrink)

We redefine a system of varieties definable by a schema of equations to include finite dimensions. Then we present a technique using ultraproducts enabling one to lift results proved for every finite dimension to the transfinite. Let \(\bf Ord\) denote the class of all ordinals. Let \(\langle \mathbf{K}_{\alpha}: \alpha\in \bf Ord\rangle\) be a system of varieties definable by a schema. Given any ordinal \(\alpha\), we define an operator \(\mathsf{Nr}_{\alpha}\) that acts on \(\mathbf{K}_{\beta}\) for any \(\beta>\alpha\) giving an algebra in \(\mathbf{K}_{\alpha}\), (...) as an abstaction of taking \(\alpha\)-neat reducts for cylindric algebras. We show that for any positive \(k\), and any infinite ordinal \(\alpha\) that \(\mathbf{S}\mathsf{Nr}_{\alpha}\mathbf{K}_{\alpha+k+1}\) cannot be axiomatized by a finite schema over \(\mathbf{S}\mathsf{Nr}_{\alpha}\mathbf{K}_{\alpha+k}\) given that the result is valid for all finite dimensions greater than some fixed finite ordinal. We apply our results to cylindric algebras and Halmos quasipolyadic algebras with equality. As an application to our algebraic result we obtain a strong incompleteness theorem (in the sense that validitities are not captured by finitary Hilbert style axiomatizations) for an algebraizable extension of \(L_{\omega,\omega}\). (shrink)

Every day, thousands of polls, surveys, and rating scales are employed to elicit the attitudes of humankind. Given the ubiquitous use of these instruments, it seems we ought to have firm answers to what is measured by them, but unfortunately we do not. To help remedy this situation, we present a novel approach to investigate the nature of attitudes. We created a self-transforming paper survey of moral opinions, covering both foundational principles, and current dilemmas hotly debated in the media. This (...) survey used a magic trick to expose participants to a reversal of their previously stated attitudes, allowing us to record whether they were prepared to endorse and argue for the opposite view of what they had stated only moments ago. The result showed that the majority of the reversals remained undetected, and a full 69% of the participants failed to detect at least one of two changes. In addition, participants often constructed coherent and unequivocal arguments supporting the opposite of their original position. These results suggest a dramatic potential for flexibility in our moral attitudes, and indicates a clear role for self-attribution and post-hoc rationalization in attitude formation and change. (shrink)

Thats logic. LEWIS CARROLL, Through the Looking Glass 1-1. The fundamental problem of this work is the question of the nature of scientific inference.

Artificial Intelligence-as-a-Service empowers individuals and organisations to access AI on-demand, in either tailored or ‘off-the-shelf’ forms. However, institutional separation between development, training and deployment can lead to critical opacities, such as obscuring the level of human effort necessary to produce and train AI services. Information about how, where, and for whom AI services have been produced are valuable secrets, which vendors strategically disclose to clients depending on commercial interests. This article provides a critical analysis of how AIaaS vendors manipulate the (...) visibility of human labour in AI production based on whether the vendor relies on paid or unpaid labour to fill interstitial gaps. Where vendors are able to occlude human labour in the organisational ‘backstage,’ such as in data preparation, validation or impersonation, they do so regularly, further contributing to ongoing techno-utopian narratives of AI hype. Yet, when vendors must co-produce the AI service with the client, such as through localised AI training, they must ‘lift the curtain’, resulting in a paradoxical situation of needing to both perpetuate dominant AI hype narratives while emphasising AI’s mundane limitations. (shrink)

In this short paper, we describe another class of forcing notions which preserve measurability of a large cardinal $\kappa$ from the optimal hypothesis, while adding new unbounded subsets to $\kappa$. In some ways these forcings are closer to the Cohen-type forcings—we show that they are not minimal—but, they share some properties with treelike forcings. We show that they admit fusion-type arguments which allow for a uniform lifting argument.

Seungbae Park argues that Bas van Fraassen’s rejection of inference to the best explanation (IBE) is problematic for his contextual theory of explanation because van Fraassen uses IBE to support the contextual theory. This paper provides a defense of van Fraassen’s views from Park’s objections. I point out three weaknesses of Park’s objection against van Fraassen. First, van Fraassen may be perfectly content to accept the implications that Park claims to follow from his views. Second, even if van Fraassen (...) rejects IBE he may still endorse particular arguments that instantiate IBE. Third, van Fraassen does not, in fact, use IBE to support his contextual theory. (shrink)

We survey the meta-ethical tools and institutional processes that traditional Islamic ethicists apply when deliberating on bioethical issues. We present a typology of these methodological elements, giving particular attention to the meta-ethical techniques and devices that traditional Islamic ethicists employ in the absence of decisive or univocal authoritative texts or in the absence of established transmitted cases. In describing how traditional Islamic ethicists work, we demonstrate that these experts possess a variety of discursive tools. We find that the ethical responsa—i.e., (...) the products of the application of the tools that we describe—are generally characterized by internal consistency. We also conclude that Islamic ethical reasoning on bioethical issues, while clearly scripture-based, is also characterized by strong consequentialist elements and possesses clear principles-based characteristics. The paper contributes to the study of bioethics by familiarizing non-specialists in Islamic ethics with the role, scope, and applicability of key Islamic ethical concepts, such as “aims” (maqāṣid), “universals” (kulliyyāt), “interest” (maṣlaḥa), “maxims” (qawā`id), “controls” (ḍawābit), “differentiators” (furūq), “preponderization” (tarjīḥ), and “extension” (tafrī`). (shrink)

Defenders of Inference to the Best Explanation claim that explanatory factors should play an important role in empirical inference. They disagree, however, about how exactly to formulate this role. In particular, they disagree about whether to formulate IBE as an inference rule for full beliefs or for degrees of belief, as well as how a rule for degrees of belief should relate to Bayesianism. In this essay I advance a new argument against non-Bayesian versions of IBE. My (...) argument focuses on cases in which we are concerned with multiple levels of explanation of some phenomenon. I show that in many such cases, following IBE as an inference rule for full beliefs leads to deductively inconsistent beliefs, and following IBE as a non-Bayesian updating rule for degrees of belief leads to probabilistically incoherent degrees of belief. (shrink)

This paper discusses the nature and the status of inference to the best explanation. We outline the foundational role given IBE by its defenders and the arguments of critics who deny it any place at all ; argue that, on the two main conceptions of explanation, IBE cannot be a foundational inference rule ; sketch an account of IBE that makes it contextual and dependent on substantive empirical assumptions, much as simplicity seems to be ; show how that (...) account avoids the critics ' complaints and leaves IBE an important role ; and sketch how our account can clarify debates over IBE in arguments for scientific realism. (shrink)

Original and penetrating, this book investigates of the notion of inference from signs, which played a central role in ancient philosophical and scientific method. It examines an important chapter in ancient epistemology: the debates about the nature of evidence and of the inferences based on it--or signs and sign-inferences as they were called in antiquity. As the first comprehensive treatment of this topic, it fills an important gap in the histories of science and philosophy.

How do we go about weighing evidence, testing hypotheses, and making inferences? The model of " inference to the best explanation " -- that we infer the hypothesis that would, if correct, provide the best explanation of the available evidence--offers a compelling account of inferences both in science and in ordinary life. Widely cited by epistemologists and philosophers of science, IBE has nonetheless remained little more than a slogan. Now this influential work has been thoroughly revised and updated, and (...) features a new introduction and two new chapters. Inference to the Best Explanation is an unrivaled exposition of a theory of particular interest in the fields both of epistemology and the philosophy of science. (shrink)

In this article, I will provide a critical overview of the form of non-deductive reasoning commonly known as “Inference to the Best Explanation” (IBE). Roughly speaking, according to IBE, we ought to infer the hypothesis that provides the best explanation of our evidence. In section 2, I survey some contemporary formulations of IBE and highlight some of its putative applications. In section 3, I distinguish IBE from C.S. Peirce’s notion of abduction. After underlining some of the essential elements of (...) IBE, the rest of the entry is organized around an examination of various problems that IBE confronts, along with some extant attempts to address these problems. In section 4, I consider the question of when a fact requires an explanation, since presumably IBE applies only in cases where some explanation is called for. In section 5, I consider the difficult question of how we ought to understand IBE in light of the fact that among philosophers, there is significant disagreement about what constitutes an explanation. In section 6, I consider different strategies for justifying the truth-conduciveness of the explanatory virtues, e.g., simplicity, unification, scope, etc., criteria which play an indispensable role in any given application of IBE. In section 7, I survey some of the most recent literature on IBE, much of which consists of investigations of the status of IBE from the standpoint of the Bayesian philosophy of science. (shrink)

We argue in Roche and Sober (2013) that explanatoriness is evidentially irrelevant in that Pr(H | O&EXPL) = Pr(H | O), where H is a hypothesis, O is an observation, and EXPL is the proposition that if H and O were true, then H would explain O. This is a “screening-off” thesis. Here we clarify that thesis, reply to criticisms advanced by Lange (2017), consider alternative formulations of Inference to the Best Explanation, discuss a strengthened screening-off thesis, and consider (...) how it bears on the claim that unification is evidentially relevant. (shrink)

Inferences from the absence of evidence to something are common in ordinary speech, but when used in scientific argumentations are usually considered deficient or outright false. Yet, as demonstrated here with the help of various examples, archaeologists frequently use inferences and reasoning from absence, often allowing it a status on par with inferences from tangible evidence. This discrepancy has not been examined so far. The article analyses it drawing on philosophical discussions concerning the validity of inference from absence, using (...) probabilistic models that were originally developed to show that such inferences are weak and inconclusive. The analysis reveals that inference from absence can indeed be justified in many important situations of archaeological research, such as excavations carried out to explore the past existence and time-span of sedentary human habitation. The justification is closely related to the fact that archaeology explores the human past via its material remains. The same analysis points to instances where inference from absence can have comparable validity in other historical sciences, and to research questions in which archaeological inference from absence will be problematic or totally unwarranted. (shrink)

How do we go about weighing evidence, testing hypotheses, and making inferences? According to the model of _Inference to the Best Explanation_, we work out what to infer from the evidence by thinking about what would actually explain that evidence, and we take the ability of a hypothesis to explain the evidence as a sign that the hypothesis is correct. In _Inference to the Best Explanation_, Peter Lipton gives this important and influential idea the development and assessment it deserves. The (...) second edition has been substantially enlarged and reworked, with a new chapter on the relationship between explanation and Bayesianism, and an extension and defence of the account of contrastive explanation. It also includes an expanded defence of the claims that our inferences really are guided by diverse explanatory considerations, and that this pattern of inference can take us towards the truth. This edition of _Inference to the Best Explanation_ has also been updated throughout and includes a new bibliography. (shrink)

This paper treats the political and ethical issues associated with the new caretaking technologies. Given the number of feminists who have raised serious concerns about the future of care work in the United States, and who have been critical of the degree to which society “free rides” on women's caretaking labor, I consider whether technology may provide a solution to this problem. Certainly, if we can create machines and robots to take on particular tasks, we may lighten the care burden (...) that women currently face, much of which is heavy and repetitious, and which results in injury and care “burnout” for many female caretakers. Yet, in some contexts, I argue that high-tech robotic care may undermine social relationships, cutting individuals off from the possibility of social connectedness with others. (shrink)

We investigate the problem how to lift the non - $\forall \Sigma^b_1(\alpha)$ - conservativity of $T^2_2(\alpha)$ over $S^2_2(\alpha)$ to the expected non - $\forall \Sigma^b_i(\alpha)$ - conservativity of $T^{i+1}_2(\alpha)$ over $S^{i+1}_2(\alpha)$ , for $i > 1$ . We give a non-trivial refinement of the “lifting method” developed in [4,8], and we prove a sufficient condition on a $\forall \Sigma^b_1(f)$ -consequence of $T_2(f)$ to yield the non-conservation result. Further we prove that Ramsey's theorem, a $\forall \Sigma^b_1(\alpha)$ - formula, is not provable (...) in $T^1_2(\alpha)$ , and that $\forall \Sigma^b_j(\alpha)$ - conservativity of $T^{i+1}_2(\alpha)$ over $T^{i}_2(\alpha)$ implies $\forall \Sigma^b_j(\alpha)$ - conservativity of the whole $T_2(\alpha)$ over $T^{i}_2(\alpha)$ , for any $j \geq 2$. (shrink)

Filipe Drapeau Vieira Contim,Pascal Ludwig | : La plupart des théoriciens de l’identité des types souscrivent à un physicalisme a posteriori à l’égard des propriétés phénoménales. Selon cette conception, les énoncés d’identité esprit/cerveau peuvent être justifiés par une inférence à la meilleure explication (IME) partant du fait empirique des corrélations esprit/cerveau. Nous soutenons que la théorie de l’identité ne peut pas s’appuyer sur cette méthodologie abductive. Nous montrons tout d’abord que l’on ne peut pas justifier les énoncés d’identité esprit/cerveau au (...) moyen d’une IME partant des corrélations esprit/cerveau car cette stratégie conduit à un dilemme : ou bien les corrélations ne sont pas des explananda, ou bien les identités esprit/cerveau doivent être admises comme des faits bruts au même titre que les lois dualistes. Nous montrons ensuite que ces énoncés d’identité peuvent être néanmoins justifiés par une IME partant du pouvoir causal des états phénoménaux. Cette seconde stratégie n’est toutefois d’aucune aide pour la forme a posteriori de théorie de l’identité ici discutée dans la mesure où elle débouche sur un physicalisme de type a priori. | : Most type identity theorists endorse a posteriori physicalism about phenomenal properties. On such a view, mind/brain identity statements can be justified by an inference to the best explanation (IBE) starting from the empirical premise of mind/brain correlations. We contend that Identity Theory cannot be based on such an abductive methodology. First, we argue that mind/brain identity statements cannot be justified by an IBE from correlations as it leads to the following dilemma : either correlations are trivial facts that cannot pretend to the status of explananda, or mind/brain identities must be admitted as brute facts, just like dualist laws. Second, we show that these identity statements can still be justified by an IBE starting from the premise of mental causation. However, this strategy is of no help for the a posteriori brand of Identity Theory here challenged since the same premise forces one to embrace a priori physicalism. (shrink)

The main motivation of the paper lies in an argument which shows the relevance of the topological notion of lifting for semantic theory. After a brief examination of aspects of knowledge which are described by means of concepts of algebraic geometry, the development of a functorial connection between topology and group theory is related to aspects of logical analysis. In categorical terms, lifting is, with extension, a form of division. As such it is investigated here, starting from simple examples in (...) general topology up to fiber spaces and topoi, in order to appreciate the recurrent pattern, which is finally used to explain the understanding of sentences about abstract domains. (shrink)