The eco-cognitive model of abduction: Ἀπαγωγή now: Naturalizing the logic of abduction

Abduction (ἀπαγωγή, in ancient Greek, often translated as “leading away” or “reduction”) is a procedure in which something that lacks classical explanatory epistemic virtue can be accepted because it has virtue of another kind: Gabbay and Woods [15] contend (GW-schema) that abduction presents an ignorance-preserving or (ignorance-mitigating) character. From this perspective abductive reasoning is a response to an ignorance-problem; through abduction the basic ignorance – that does not have to be considered a total “ignorance” – is neither solved nor left intact. Abductive reasoning is an ignorance-preserving accommodation of the problem at hand. Is abduction really ignorance-preserving? To better answer this question I will introduce (and take advantage of) an eco-cognitive model (EC-Model) of abduction. It will be illustrated that through abduction, knowledge can be enhanced, even when abduction is not considered an inference to the best explanation in the classical sense of the expression, that is an inference necessarily characterized by an empirical evaluation phase, or an inductive phase, as Peirce called it. To further deepen the eco-cognitive character of abduction a simple genealogy of logic is provided: Aristotle clearly states that in syllogistic theory local/environmental cognitive factors – external to that peculiar inferential process, for example regarding users/reasoners, are given up. Indeed, to define syllogism Aristotle first of all insists that all syllogisms are valid and contends that the necessity of this kind of reasoning is related to the circumstance that “no further term from outside (ἔξωθɛν) is needed”, in sum syllogism is the fruit of a kind of eco-cognitive immunization. At the same time Aristotle presents a seminal perspective on abduction: the second part of the article considers the famous passage in Chapter B25 of Prior Analytics concerning ἀπαγωγή (“leading away”), also studied by Peirce. I contend that some of the current well-known distinctive characters of abductive cognition are already expressed, which are in tune with the EC-Model. By providing an illustration of the role of the method of analysis and of the middle terms in Plato's dialectic argumentation, considered as related to the diorismic/poristic process in ancient geometry – also, later on, emphasized by Proclus – I maintain that it is just this intellectual heritage which informs Aristotle' Chapter B25 on ἀπαγωγή. Even if, in general, Aristotle seems to sterilize, thanks to the invention of syllogistic theory, every “dialectic” background of reasoning, nevertheless in Chapter B25 he is still pointing to the fundamental inferential role in reasoning of those externalities that substantiate the process of “leading away” (ἀπαγωγή). Hence, we can gain a new positive perspective about the “constitutive” eco-cognitive character of abduction, just thanks to Aristotle himself. Finally, the paper presents an excursus on Aristotle's enthymemes from signs, disregarded by Peirce, but extremely important to stress the Aristotelian treatment of what I have called selective abduction. A forthcoming companion paper [35] will further deepen the EC-Model of abduction stressing stricter logical aspects: the first result will be that, contrarily to the classical logical view, relevance and plausibility in abductive reasoning have to be relativized and so the epistemologically embarrassing concepts of irrelevance and implausibility exculpated: they are not always offensive to reason.     

Transition semantics: the dynamics of dependence logic

We examine the relationship between dependence logic and game logics. A variant of dynamic game logic, called Transition Logic, is developed, and we show that its relationship with dependence logic is comparable to the one between first-order logic and dynamic game logic discussed by van Benthem. This suggests a new perspective on the interpretation of dependence logic formulas, in terms of assertions about reachability in games of imperfect information against Nature. We then capitalize on this intuition by developing expressively equivalent variants of dependence logic in which this interpretation is taken to the foreground.     

Positional Order and Group Size Effects in Resource Dilemmas with Uncertain Resources

We report the results of three experiments in which groups of players share a common resource pool whose size is a random variable with a commonly known distribution. We study a new information structure - called the positional order protocol - under which requests are made in an exogenously determined and commonly known order without disclosing the requests of previous players in the sequence. Mean individual requests under this protocol of play are compared with data gathered under the more familiar simultaneous protocol (simultaneously made requests) and sequential protocol (sequentially made requests with full disclosure of previous requests). Previously reported effects of the resource uncertainty on individual requests obtained under the simultaneous and sequential protocols are generalized across different group sizes. In contrast to the game-theoretical prediction, which does not distinguish between the simultaneous and positional order protocols, mean individual requests and position in the sequence are highly and significantly correlated. We conclude that position effects can be induced by temporal priority, even in the absence of differential information.     

An empirical study of psychology and logic. Abduction and belief as normalizing habits of positive expectation

This research supports the value of psychology for the study of abduction, and the value of abduction for better understanding psychological meaning-making. More specifically, we argue that the logical structure of abduction is supported by psychological processes, namely, surprise, the psychological normalization of that surprise by a proposed explanatory hypothesis, and the projection of that hypothesis as a normalizing, interpretive lens onto related subsequent experiences. We examine how abduction can be better understood by taking into consideration what Peirce called belief, an understanding of belief that in effect reflects the psychological aspects of abduction. We also examine how abduction helps identify a line of reasoning that people follow with or without their explicit knowledge. The empirical study involves a series of semi-structured interviews focusing on the genesis of perceived loneliness and solitude as normalizing habits of positive expectation from the situation of being alone.     

Predictions from a model of global psychophysics about differences between perceptual and physical matches

A well-known phenomenon is that ??matched?? successive signals do not result in physical identity. This phenomenon has mostly been studied in terms of how much the second of two signals varies from the first, which is called the time-order error (TOE). Here, theoretical predictions led us to study the more general question of how much the matching signal differs from the standard signal, independent of the position of the matching signal as the first or second in a presentation. This we call non-equal matches (NEM). Using Luce??s (Psychological Review, 109, 520?C532, 2002, Psychological Review, 111, 446?C454, 2004, Psychological Review, 115, 601, 2008, Psychological Review, 119, 373?C387, 2012) global psychophysical theory, we predicted NEM when an intensity z is perceived to be ??1 times a standard signal x.?? The theory predicts two different types of individual behaviors for the NEM, and these predictions were evaluated and confirmed in an experiment. We showed that the traditional definition of TOE precludes the observation, and thus the study, of the NEM phenomenon, and that the NEM effect is substantial enough to alter conclusions based on data that it affects. Furthermore, we demonstrated that the custom of averaging data over individuals clearly leads to quite misleading results. An important parameter in this modeling is a reference point that plays a central role in creating variability in the data, so that the key to obtaining regular data from respondents is to stabilize the reference point.     

Gluteus medius strength, endurance, and co-activation in the development of low back pain during prolonged standing

This study measured gluteus medius (GM) strength and endurance before and after a 2 h prolonged standing task in previously asymptomatic individuals, to compare between individuals who did and did not report pain in the low back. Twenty-four participants without a history of low back pain stood in a constrained area for 2 h. Before and after the standing protocol, participant’s maximal hip abduction strength (N) and side-bridge endurance (seconds and GM myoelectric fatigue) were measured. Continuous surface EMG was collected from GM during the 2-h protocol for analysis of bilateral co-activation. Pain in the low back was rated every 15 min with a visual analog scale (VAS). Seventeen of 24 (71%) previously asymptomatic participants developed pain in the low back during the standing protocol. These participants had lower side-bridge endurance (p = .002), and higher gluteus medius (GM) co-activation (p = .002) compared to participants who did not develop pain in the low back. Hip abduction strength decreased for both groups following prolonged standing, with no between groups’ difference. Lower side-bridge endurance and hip abduction strength were significantly associated with higher GM co-activation (adjusted r² = .34), but not pain levels. Side-bridge endurance and GM co-activation, but not hip abduction strength, may have utility in identifying participants likely to develop pain in the low back during prolonged standing. The best training program for increasing GM endurance is unclear.     

Remembering kinds: new evidence that categories are privileged in children's thinking

What are the representations and learning mechanisms that underlie conceptual development? The present research provides evidence in favor of the claim that this process is guided by an early-emerging predisposition to think and learn about abstract kinds. Specifically, three studies (N = 192) demonstrated that 4- to 7-year-old children have better recall for novel information about kinds (e.g., that dogs catch a bug called “fep”) than for similar information about individuals (e.g., that a particular dog catches a bug called “fep”). By showing that children are particularly likely to retain information about kinds, this work not only provides a first empirical demonstration of a phenomenon that may be key to conceptual development but also makes it apparent that young children’s thinking is suffused with abstractions rather than being perceptually-based and concrete.     

Abductive reasoning in neural-symbolic systems

Abduction is or subsumes a process of inference. It entertains possible hypotheses and it chooses hypotheses for further scrutiny. There is a large literature on various aspects of non-symbolic, subconscious abduction. There is also a very active research community working on the symbolic (logical) characterisation of abduction, which typically treats it as a form of hypothetico-deductive reasoning. In this paper we start to bridge the gap between the symbolic and sub-symbolic approaches to abduction. We are interested in benefiting from developments made by each community. In particular, we are interested in the ability of non-symbolic systems (neural networks) to learn from experience using efficient algorithms and to perform massively parallel computations of alternative abductive explanations. At the same time, we would like to benefit from the rigour and semantic clarity of symbolic logic. We present two approaches to dealing with abduction in neural networks. One of them uses Connectionist Modal Logic and a translation of Horn clauses into modal clauses to come up with a neural network ensemble that computes abductive explanations in a top-down fashion. The other combines neural-symbolic systems and abductive logic programming and proposes a neural architecture which performs a more systematic, bottom-up computation of alternative abductive explanations. Both approaches employ standard neural network architectures which are already known to be highly effective in practical learning applications. Differently from previous work in the area, our aim is to promote the integration of reasoning and learning in a way that the neural network provides the machinery for cognitive computation, inductive learning and hypothetical reasoning, while logic provides the rigour and explanation capability to the systems, facilitating the interaction with the outside world. Although it is left as future work to determine whether the structure of one of the proposed approaches is more amenable to learning than the other, we hope to have contributed to the development of the area by approaching it from the perspective of symbolic and sub-symbolic integration.

Should the probabilities count?

When facing a choice between saving one person and saving many, some people have argued that fairness requires us to decide without aggregating numbers; rather we should decide by coin toss or some form of lottery, or alternatively we should straightforwardly save the greater number but justify this in a non-aggregating contractualist way. This paper expands the debate beyond well-known number cases to previously under-considered probability cases, in which not (only) the numbers of people, but (also) the probabilities of success for saving people vary. It is shown that, in these latter cases, both the coin toss and the lottery lead to what is called an awkward conclusion, which makes probabilities count in a problematic way. Attempts to avoid this conclusion are shown to lead into difficulties as well. Finally, it is shown that while the greater number method cannot be justified on contractualist grounds for probability cases, it may be replaced by another decision method which is so justified. This decision method is extensionally equivalent to maximising expected value and seems to be the least problematic way of dealing with probability cases in a non-aggregating manner.     

Logics for Epistemic Programs

We construct logical languages which allow one to represent a variety of possible types of changes affecting the information states of agents in a multi-agent setting. We formalize these changes by defining a notion of epistemic program. The languages are two-sorted sets that contain not only sentences but also actions or programs. This is as in dynamic logic, and indeed our languages are not significantly more complicated than dynamic logics. But the semantics is more complicated. In general, the semantics of an epistemic program is what we call aprogram model. This is a Kripke model of ‘actions’,representing the agents' uncertainty about the current action in a similar way that Kripke models of ‘states’ are commonly used in epistemic logic to represent the agents' uncertainty about the current state of the system. Program models induce changes affecting agents' information, which we represent as changes of the state model, called epistemic updates. Formally, an update consists of two operations: the first is called the update map, and it takes every state model to another state model, called the updated model; the second gives, for each input state model, a transition relation between the states of that model and the states of the updated model. Each variety of epistemic actions, such as public announcements or completely private announcements to groups, gives what we call an action signature, and then each family of action signatures gives a logical language. The construction of these languages is the main topic of this paper. We also mention the systems that capture the valid sentences of our logics. But we defer to a separate paper the completeness proof. The basic operation used in the semantics is called the update product. A version of this was introduced in Baltag et al. (1998), and the presentation here improves on the earlier one. The update product is used to obtain from any program model the corresponding epistemic update, thus allowing us to compute changes of information or belief. This point is of interest independently of our logical languages. We illustrate the update product and our logical languages with many examples throughout the paper.     

Automatic activation of attribute knowledge in heuristic inference from memory

In memory-based decision making, people often rely on simple heuristics such as take-the-best (TTB; Gigerenzer & Goldstein, Psychological Review, 103, 650–669, 1996), which processes information about the alternatives sequentially and stops processing as soon as a decision can be made. In this article, we examine the memory processes associated with TTB—in particular, to what degree the selective memory retrieval of relevant information required by TTB is accompanied by automatic activation of associated but irrelevant information. To address this question, we studied the fan effect (Anderson, Cognitive Psychology, 6, 451–474, 1974), which is assumed to arise from automatic spread of activation, in inferences from memory. Participants were instructed to use TTB when making decisions about objects on the basis of previously memorized attribute information. Both the number of attributes required by TTB and the number of attributes associated with an object (i.e., fan level) were manipulated. As it turned out, response times and the correct execution of TTB were a function not only of the number of required attributes, but also of the number of associated attributes. This suggests that information that TTB “ignores” is nevertheless activated in memory.     

Merging Inference and Conjecture by Information

The intuitive notion of a binary relation on information-bearers, comparingthem with respect to their closeness to the available information, is oftenconstrued in terms of comparing their symmetric difference with, orcompositional similarity to, the available information. This happens forinstance in some treatments of verisimilitude. We expound an abstractmathematical rendering of the relevant data-dependent relation in theframework of Boolean algebras. For every element t of a Boolean algebra B we construct the t-modulated Boolean algebra B_tin which the order relation represents `is at most as compatible with t as' or `is at best as similar to t as'. In the case of Lindenbaum-Tarskialgebras, t expresses the available information, and the compatibilityrelation turns out to be an entwinement of inferential and conjecturalrelations. It is just classical entailment when no information is available(i.e., when t is logically true) and becomes more boldly abductive themore information is available. The rich algebraic structures of a Boolean algebra –- including its Boolean group structures –- play a significant role in this combination of deduction and abduction and also induce cautious anddaring variants of the compatibility relation. Links with the literature onverisimilitude, abduction, and related topics are indicated.     

Brain activation detection by neighborhood one-class SVM

Brain activation detection is an important problem in fMRI data analysis. In this paper, we propose a data-driven activation detection method called neighborhood one-class SVM (NOC-SVM). Based on the probability distribution assumption of the one-class SVM algorithm and the neighborhood consistency hypothesis, NOC-SVM identifies a voxel as either an activated or non-activated voxel by a weighted distance between its near neighbors and a hyperplane in a high-dimensional kernel space. The proposed NOC-SVM are evaluated by using both synthetic and real datasets. On two synthetic datasets with different SNRs, NOC-SVM performs better than K-means and fuzzy K-means clustering and is comparable to POM. On a real fMRI dataset, NOC-SVM can discover activated regions similar to K-means and fuzzy K-means. These results show that the proposed algorithm is an effective activation detection method for fMRI data analysis. Furthermore, it is stabler than K-means and fuzzy K-means clustering.     

A simple computational algorithm of model-based choice preference

A broadly used computational framework posits that two learning systems operate in parallel during the learning of choice preferences—namely, the model-free and model-based reinforcement-learning systems. In this study, we examined another possibility, through which model-free learning is the basic system and model-based information is its modulator. Accordingly, we proposed several modified versions of a temporal-difference learning model to explain the choice-learning process. Using the two-stage decision task developed by Daw, Gershman, Seymour, Dayan, and Dolan (2011), we compared their original computational model, which assumes a parallel learning process, and our proposed models, which assume a sequential learning process. Choice data from 23 participants showed a better fit with the proposed models. More specifically, the proposed eligibility adjustment model, which assumes that the environmental model can weight the degree of the eligibility trace, can explain choices better under both model-free and model-based controls and has a simpler computational algorithm than the original model. In addition, the forgetting learning model and its variation, which assume changes in the values of unchosen actions, substantially improved the fits to the data. Overall, we show that a hybrid computational model best fits the data. The parameters used in this model succeed in capturing individual tendencies with respect to both model use in learning and exploration behavior. This computational model provides novel insights into learning with interacting model-free and model-based components.     

Bootstrap Contraction

We can often specify how we would contract by a certain sentence by saying that this contraction would coincide with some other contraction that we know how to perform. We can for instance clarify that our contraction by p&q would coincide with our contraction by p, or by q, or by {p, q}. In a framework where the set of potential outcomes is known, some contractions are “self-evident” in the sense that there is only one serious candidate that can be the outcome of such a contraction. Contraction by a specific contractee (sentence or set of sentences to be contracted) is bootstrapped if it is specified by saying that it coincides with some such self-evident contraction. For a wide range of (multiple) contraction operators, contractions by any contractee can be bootstrapped. This means that the selection mechanism (selection function, incision function, etc.) can be replaced by a function called a bootstrapping selector that assigns to each contractee some “self-evident” contractee that yields the same outcome. With bootstrapping we can eliminate traditional extralogical components in contraction (e.g., selection functions) and replace them by bootstrapping selectors that reflect more closely the ways in which we actually reason and argue about belief contraction.     

Pre-cognitive Semantic Information

This paper addresses one of the fundamental problems of the philosophy of information: How does semantic information emerge within the underlying dynamics of the world?—the dynamical semantic information problem. It suggests that the canonical approach to semantic information that defines data before meaning and meaning before use is inadequate for pre-cognitive information media. Instead, we should follow a pragmatic approach to information where one defines the notion of information system as a special kind of purposeful system emerging within the underlying dynamics of the world and define semantic information as the currency of the system. In this way, systems operating with semantic information can be viewed as patterns in the dynamics—semantic information is a dynamical system phenomenon of highly organized systems. In the simplest information systems, the syntax, semantics, and pragmatics of the information medium are co-defined. It proposes a new more general theory of information semantics that focuses on the interface role of the information states in the information system—the interface theory of meaning. Finally, with the new framework, it addresses the debate between weakly semantic and strongly semantic accounts of information, siding with the strongly semantic view because the pragmatic account developed here is a better generalization of it.     

Technique determinants of knee joint loads during cutting in female soccer players

The aim of this study was to investigate the relationships between technique characteristics and knee abduction moments during 90° cuts. A cross sectional design involving 26 elite and sub-elite female soccer players (mean ± SD; age: 21 ± 3.2 years, height: 1.68 ± 0.07 m, and mass: 59.1 ± 6.8 kg) was used to explore relationships between pre-determined technical factors on knee abduction moments during cutting. Three dimensional motion analyses of 90° cuts on the right leg were performed using ‘Qualisys Pro Reflex’ infrared cameras (240 Hz). Ground reaction forces were collected from two AMTI force platforms (1200 Hz) embedded into the running track to examine 2nd last and last footfalls. Pearson’s correlation coefficients, co-efficients of determination and hierarchical multiple regression were used to explore relationships between a range of technique parameters and peak knee abduction moments. Significance was set at p < .05. Hierarchical multiple regression revealed that initial knee abduction angle, lateral leg plant distance and initial lateral trunk lean could explain 67% (62% adjusted) of the variation in peak knee abduction moments (F_(1,22) = 8.869, p = .007). These findings reveal potential modifiable technical factors to lower peak knee abduction moments during cutting.     

An Impossibility Result for Coherence Rankings

If we receive information from multiple independent and partially reliable information sources, then whether we are justified to believe these information items is affected by how reliable the sources are, by how well the information coheres with our background beliefs and by how internally coherent the information is. We consider the following question. Is coherence a separable determinant of our degree of belief, i.e. is it the case that the more coherent the new information is, the more justified we are in believing the new information, ceteris paribus? We show that if we consider sets of information items of any size (Holism), and if we assume that there exists a coherence Ordering over such sets and that coherence is a function of the probability distribution over the propositions in such sets (Probabilism), then Separability fails to hold.