The two volumes in this advanced textbook present results, proof methods, and translations of motivational and philosophical considerations to formal constructions. In the associated Vol. I the author explains preferential structures and abstract size. In this Vol. II he presents chapters on theory revision and sums, defeasible inheritance theory, interpolation, neighbourhood semantics and deontic logic, abstract independence, and various aspects of nonmonotonic and other logics. In both volumes the text contains many exercises and some solutions, and the author limits the (...) discussion of motivation and general context throughout, offering this only when it aids understanding of the formal material, in particular to illustrate the path from intuition to formalisation. Together these books are a suitable compendium for graduate students and researchers in the area of computer science and mathematical logic. (shrink)

The epistemology of intuitions has become popular recently with philosophers’ increasing use of experimental methods to study intuitions. Philosophers have focused on the reliability of intuitions, as empirical studies seem to suggest that conflicting intuitions are common. One set of studies, concerning what Sinnott-Armstrong calls the abstract/concrete paradox, suggests that conflicting intuitions are common and, hence, that mistaken intuitions are common. As Goldman notes, if mistaken intuitions are sufficiently prevalent, then we might have reason to think intuitions are unreliable. I (...) argue that mistaken intuitions are not common, since studies concerning the abstract/concrete paradox have unknowingly studied several distinct phenomena instead of the abstract/concrete paradox and, hence, that they present merely apparently conflicting intuitions. I then discuss the import of empirical studies for debates about reliability, noting that those studies can inform us about the unreliability of intuitions but we are still unclear about the conditions for reliability. (shrink)

This paper contains a joint study of two sentential logics that combine a many-valued character, namely tetravalence, with a modal character; one of them is normal and the other one quasinormal. The method is to study their algebraic counterparts and their abstract models with the tools of Abstract Algebraic Logic, and particularly with those of Brown and Suszko's theory of abstract logics as recently developed by Font and Jansana in their "A General Algebraic Semantics for Sentential Logics". The logics (...) studied here arise from the algebraic and lattice-theoretical properties we review of Tetravalent Modal Algebras, a class of algebras studied mainly by Loureiro, and also by Figallo, Landini and Ziliani, at the suggestion of the late Antonio Monteiro. (shrink)

While the fundamental laws of physics are time-reversal invariant, most macroscopic processes are irreversible. Given that the fundamental laws are taken to underpin all other processes, how can the fundamental time-symmetry be reconciled with the asymmetry manifest elsewhere? In statistical mechanics, progress can be made with this question. What I dub the ‘Zwanzig–Zeh–Wallace framework’ can be used to construct the irreversible equations of SM from the underlying microdynamics. Yet this framework uses coarse-graining, a procedure that has faced much criticism. I (...) focus on two objections in the literature: claims that coarse-graining makes time-asymmetry ‘illusory’ and ‘anthropocentric’. I argue that these objections arise from an unsatisfactory justification of coarse-graining prevalent in the literature, rather than from coarse-graining itself. This justification relies on the idea of measurement imprecision. By considering the role that abstraction and autonomy play, I provide an alternative justification and offer replies to the illusory and anthropocentric objections. Finally, I consider the broader consequences of this alternative justification: the connection to debates about inter-theoretic reduction and the implication that the time-asymmetry in SM is weakly emergent. 1Introduction 1.1Prospectus2The Zwanzig–Zeh–Wallace Framework3Why Does This Method Work? 3.1The special conditions account3.2When is a density forwards-compatible?4Anthropocentrism and Illusion: Two Objections 4.1The two objections in more detail4.2Against the justification by measurement imprecision5An Alternative Justification 5.1Abstraction and autonomy5.2An illustration: the Game of Life6Reply to Illusory7Reply to Anthropocentric8The Wider Landscape: Concluding Remarks 8.1Inter-theoretic relations8.2The nature of irreversibility. (shrink)

We generalise the Blok–Jónsson account of structural consequence relations, later developed by Galatos, Tsinakis and other authors, in such a way as to naturally accommodate multiset consequence. While Blok and Jónsson admit, in place of sheer formulas, a wider range of syntactic units to be manipulated in deductions (including sequents or equations), these objects are invariablyaggregatedvia set-theoretical union. Our approach is more general in that nonidempotent forms of premiss and conclusion aggregation, including multiset sum and fuzzy set union, are considered. (...) In their abstract form, thus,deductive relationsare defined as additional compatible preorderings over certain partially ordered monoids. We investigate these relations using categorical methods and provide analogues of the main results obtained in the general theory of consequence relations. Then we focus on the driving example of multiset deductive relations, providing variations of the methods of matrix semantics and Hilbert systems in Abstract Algebraic Logic. (shrink)

In this paper, I explore the approaches to methodological abstraction and self-alienation developed respectively in Karl Mannheim’s early sociology of intellectuals and in Edmund Husserl’s late transcendental phenomenology. In Mannheim’s early and experimental works, the resistance to abstraction and alienation is located in a stratum of intellectuals able to meaningfully combine diverse cultural currents in a social process of cultivation (Bildung). In Husserl, to contrast, this resistance is grasped as a constant crisis in the methods of pursuing philosophical (...) truth. While these approaches seem difficult to reconcile, I suggest in closing that this difficulty can be related to their shared emphasis on a theoretical response to the practical and historical reality of self-alienation. (shrink)

Abstractionist programs in the philosophy of mathematics have focused on abstraction principles, taken as implicit definitions of the objects in the range of their operators. In second-order logic (SOL) with predicative comprehension, such principles are consistent but also (individually) mathematically weak. This paper, inspired by the work of Boolos (Proceedings of the Aristotelian Society 87, 137–151, 1986) and Zalta (Abstract Objects, vol. 160 of Synthese Library, 1983), examines explicit definitions of abstract objects. These axioms state that there is a (...) unique abstract encoding all concepts satisfying a given formula $$\phi (F)$$, with F a concept variable. Such a system is inconsistent in full SOL. It can be made consistent with several intricate tweaks, as Zalta has shown. Our approach in this article is simpler: we use a novel method to establish consistency in a restrictive version of predicative SOL. The resulting system, RPEAO, interprets first-order PA in extensional contexts, and has a natural extension delivering a peculiar interpretation of PA $$^2$$. (shrink)

Bayesian decision theory provides a simple formal elucidation of some of the ways that representation and representational abstraction are involved with, and exploit, both prediction and its rather distant cousin, predictive coding. Both model-free and model-based methods are involved.

One of the key features of modern mathematics is the adoption of the abstract method. Our goal in this paper is to propose an explication of that method that is rooted in the history of the subject.

Kripke’s notion of groundedness plays a central role in many responses to the semantic paradoxes. Can the notion of groundedness be brought to bear on the paradoxes that arise in connection with abstraction principles? We explore a version of grounded abstraction whereby term models are built up in a ‘grounded’ manner. The results are mixed. Our method solves a problem concerning circularity and yields a ‘grounded’ model for the predicative theory based on Frege’s Basic Law V. However, (...) the method is poorly behaved unless the background second-order logic is predicative. (shrink)

A possibility of defining logical constants within abstract logical frameworks is discussed, in relation to abstract definition of logical consequence. We propose using duals as a general method of applying the idea of invariance under replacement as a criterion for logicality.

We study classes of right-angled Coxeter groups with respect to the strong submodel relation of a parabolic subgroup. We show that the class of all right-angled Coxeter groups is not smooth and establish some general combinatorial criteria for such classes to be abstract elementary classes (AECs), for them to be finitary, and for them to be tame. We further prove two combinatorial conditions ensuring the strong rigidity of a right-angled Coxeter group of arbitrary rank. The combination of these results translates (...) into a machinery to build concrete examples of AECs satisfying given model-theoretic properties. We exhibit the power of our method by constructing three concrete examples of finitary classes. We show that the first and third classes are nonhomogeneous and that the last two are tame, uncountably categorical, and axiomatizable by a single Lω1,ω-sentence. We also observe that the isomorphism relation of any countable complete first-order theory is κ-Borel reducible (in the sense of generalized descriptive set theory) to the isomorphism relation of the theory of right-angled Coxeter groups whose Coxeter graph is an infinite random graph. (shrink)

Abstract State Machines (ASMs) provide a formal method for transparent design and specification of complex dynamic systems. They combine advantages of informal and formal methods. Applications of this method motivate a number of computability and decidability problems connected to ASMs. Such problems result for example from the area of verifying properties of ASMs. Their high expressive power leads rather directly to undecidability respectively uncomputability results for most interesting problems in the case of unrestricted ASMs. Consequently, it is rather (...) natural to ask whether there exist expressive classes of ASMs for which we can prove positive decidability and computability results. In this work, we introduce such a class of ASMs. The concept is similar to the one of the guarded fragment of first-order logic. We analyze the expressive power of this class and prove that it is stronger than Datalog LITE and the guarded fragment of first-order fixed point logic. Some decidability and computability results have been proven in earlier works. (shrink)

In this paper we study an alternative approach to the concept of abstract logic and to connectives in abstract logics. The notion of abstract logic was introduced by Brown and Suszko —nevertheless, similar concepts have been investigated by various authors. Considering abstract logics as intersection structures we extend several notions to their κ -versions, introduce a hierarchy of κ -prime theories, which is important for our treatment of infinite connectives, and study different concepts of κ -compactness. We are particularly interested (...) in non-topped intersection structures viewed as semi-lattices with a minimal meet-dense subset, i.e., with a minimal generator set. We study a chain condition which is sufficient for a minimal generator set, implies compactness of the logic, and in regular logics is equivalent to compactness of the consequence relation together with the existence of a inconsistent set, where κ is the cofinality of the cardinality of the logic. Some of these results are known in a similar form in the context of closure spaces, we give extensions to intersection structures and to big cardinals presenting new proofs based on set-theoretical tools. The existence of a minimal generator set is crucial for our way to define connectives. Although our method can be extended to further non-classical connectives we concentrate here on intuitionistic and infinite ones. Our approach leads us to the concept of the set of complete theories which is stable under all considered connectives and gives rise to the definition of the topological space of the logic. Topological representations of abstract logics by means of this space remain to be further investigated. (shrink)

L’objectif de cet article est de montrer que la réflexion engagée par Jules Vuillemin sur les structures algébriques dans les années 1960 lui permettra de dégager une conception structurale de l’abstraction, dont il tirera une compréhension nomologique de l’objectivité. Ces deux concepts seront alors convoqués bien des années plus tard pour proposer une construction de l’espace représentatif, que Vuillemin conçoit comme une réfutation de l’idéalisme matériel de Berkeley. La possibilité de retracer la genèse de nos notions spatiales et de (...) leur garantir une certaine objectivité serait ainsi rendue possible par un emprunt aux méthodes de l’algèbre moderne, conformément à l’esprit de La Philosophie de l’algèbre. (shrink)

We argue that two powerful error-theoretic concepts provide a general framework that satisfactorily accounts for key aspects of the explanation of physical patterns. This method gives an objective criterion to determine which mathematical models in a class of neighboring models are just as good as the exact one. The method also emphasizes that abstraction is essential for explanation and provides a precise conceptual framework that determines whether a given abstraction is explanatorily relevant and justified. Hence, it (...) increases our epistemological understanding of how one should go about reconstructing scientific practices by making clear that, at a fundamental level, a key aspect of mathematical modeling consists in exactly solving nearby problems. (shrink)

For Viennese artist Florian Pumhösl »abstraction is a method«, not a category. Or rather, if abstraction is the defining category of modernism, the objective is to reproduce modernism's problems and limits and exploit relationships among its parts. Considering what Pumhösl calls the »textile complex« of modernism, this essay examines the artist's work in parallel with Charles Sanders Peirce's diagram concept and Gottfried Semper's use of textile diagrams throughout Style in the Technical and Tectonic Arts.

Journal Name: Cognitive Linguistics Issue: Ahead of print.

The cofinality quantifiers were introduced by Shelah as an example of a compact logic stronger than first-order logic. We show that the classes of models axiomatized by these quantifiers can be turned into an Abstract Elementary Class by restricting to positive and deliberate uses. Rather than using an ad hoc proof, we give a general framework of abstract Skolemizations. This method gives a uniform proof that a wide rang of classes are Abstract Elementary Classes.

We suggest a method of finding a notion of type to abstract elementary classes and determine under what assumption on these types the class has a well-behaved homogeneous and universal "monster" model, where homogeneous and universal are defined relative to our notion of type.

The organizers and members of the international abstract review committee conducted anonymous review of all abstracts from the conference for merit based on relevance, originality, strength and clarity of methods and analyses, and overall contribution to the field of neuroethics. Here, we proudly introduce the collection of 21 top-ranked abstracts for the poster contest.

> Context • The alleged dichotomy between mind and matter is pervasive. Therefore, the attempt to explain mat- ter in terms of mind (idealism) is often considered a mirror image of that of explaining mind in terms of mat- ter (mainstream physicalism), in the sense of being structurally equivalent despite being reversely arranged. > Problem • I argue that this is an error arising from language artifacts, for dichotomies must reside in the same level of abstraction. > Method (...) • I show that, because matter outside mind is not an empirical observation but rather an explanatory model, the epistemic symmetry between the two is broken. Consequently, matter and mind cannot reside in the same level of abstraction. > Results • It then becomes clear that attempting to explain mind in terms of matter is epistemically more costly than attempting to explain matter in terms of mind. > Implications • The qualities of experience are suggested to be not only epistemically, but also ontologically primary. > Constructivist content • I high- light the primacy of perceptual constructs over explanatory abstraction on both epistemic and ontic levels. > Key words • Idealism, physicalism, pancomputationalism, anti-realism, hard problem of consciousness, epistemic symmetry, explanatory abstraction, levels of abstraction. (shrink)

In their review, Ruba and Repacholi summarize the methods used to assess preverbal infants’ understanding of emotions, and analyze the existing evidence in light of classical and constructionist ac...

This paper presents a methodology to design and implement programs intended to decide cases, described as sets of factors, according to a theory of a particular domain based on a set of precedent cases relating to that domain. We useDialectical Frameworks, a recent development in AI knowledge representation, as the central feature of our design method. ADFs will play a role akin to that played by Entity–Relationship models in the design of database systems. First, we explain how the factor (...) hierarchy of the well-known legal reasoning system CATO can be used to instantiate an ADF for the domain of US Trade Secrets. This is intended to demonstrate the suitability of ADFs for expressing the design of legal cased based systems. The method is then applied to two other legal domains often used in the literature of AI and Law. In each domain, the design is provided by the domain analyst expressing the cases in terms of factors organised into an ADF from which an executable program can be implemented in a straightforward way by taking advantage of the closeness of the acceptance conditions of the ADF to components of an executable program. We evaluate the ease of implementation, the performance and efficacy of the resulting program, ease of refinement of the program and the transparency of the reasoning. This evaluation suggests ways in which factor based systems, which are limited by taking as their starting point the representation of cases as sets of factors and so abstracting away the particular facts, can be extended to address open issues in AI and Law by incorporating the case facts to improve the decision, and by considering justification and reasoning using portion of precedents. (shrink)

It is not only in science that abstraction is found as a method of dealing with the world, and we may profitably begin by showing its wide use in ordinary practical life.

Natural language processing techniques contribute more and more in analyzing legal documents recently, which supports the implementation of laws and rules using computers. Previous approaches in representing a legal sentence often based on logical patterns that illustrate the relations between concepts in the sentence, often consist of multiple words. Those representations cause the lack of semantic information at the word level. In our work, we aim to tackle such shortcomings by representing legal texts in the form of abstract meaning representation, (...) a graph-based semantic representation that gains lots of polarity in NLP community recently. We present our study in AMR Parsing and AMR-to-text Generation specifically for legal domain. We also introduce JCivilCode, a human-annotated legal AMR dataset which was created and verified by a group of linguistic and legal experts. We conduct an empirical evaluation of various approaches in parsing and generating AMR on our own dataset and show the current challenges. Based on our observation, we propose our domain adaptation method applying in the training phase and decoding phase of a neural AMR-to-text generation model. Our method improves the quality of text generated from AMR graph compared to the baseline model. 2018; and “Legal Text Generation fromMeaning Representation”, published in the 32nd International Conference on Legal Knowledge and Information Systems 2019.). (shrink)

Since the beginning of the twentieth century, abstract art has formed a central stream of modern art. To attain purely aesthetic goals, many avant-garde artists turned painting in particular into a pursuit of breaking off the relations with natural forms. Instead of copying them, they have merely relied on their inner visions. When externalizing these visions directly on the canvas or sheets of paper, the practitioners of abstract art have inadvertently used the phenomenological method and its epoché. In this (...) essay I argue that the philosophies of Kupka and Husserl are largely compatible. This is not because the two use the same terminology, but because they virtually mean and do the same thing in their respective fields. Even where there are significant differences between them, these are not as great as it might at first seem. In the essay’s conclusion I sum up some of the most significant implications their compatible theories have for the philosophy of art and for various theories of art today. (shrink)

IntroductionThe abstracts of a conference are important for informing the participants about the results that are communicated. However, there is poor reporting in conference abstracts in disability research. This paper aims to assess the reporting in the abstracts presented at the 5th African Network for Evidence-to-Action in Disability (AfriNEAD) Conference in Ghana.MethodsThis descriptive study extracted information from the abstracts presented at the 5th AfriNEAD Conference. Three reviewers independently reviewed all the included abstracts using a predefined data extraction form. Descriptive statistics (...) were used to analyze the extracted information, using Stata version 15.ResultsOf the 76 abstracts assessed, 54 met the inclusion criteria, while 22 were excluded. More than half of all the included abstracts (32/54; 59.26%) were studies conducted in Ghana. Some of the included abstracts did not report on the study design (37/54; 68.5%), the type of analysis performed (30/54; 55.56%), the sampling (27/54; 50%), and the sample size (18/54; 33.33%). Almost all the included abstracts did not report the age distribution and the gender of the participants.ConclusionThe study findings confirm that there is poor reporting of methods and findings in conference abstracts. Future conference organizers should critically examine abstracts to ensure that these issues are adequately addressed, so that findings are effectively communicated to participants. (shrink)

Molecular biologists use different kinds of reasoning strategies for different tasks, such as hypothesis formation, experimental design, and anomaly resolution. More specifically, the reasoning strategies discussed in this paper may be characterized as (1) abstraction-instantiation, in which an abstract skeletal model is instantiated to produce an experimental system; (2) the systematic scan, in which alternative hypotheses are systematically generated; and (3) modular anomaly resolution, in which components of a model are stated explicitly and methodically changed to generate alternative changes (...) to resolve an anomaly. This work grew out of close observation over a period of six months of an actively functioning molecular genetics laboratory. (shrink)

The dangers of character reification for cladistic inference are explored. The identification and analysis of characters always involves theory-laden abstraction—there is no theory-free “view from nowhere.” Given theory-ladenness, and given a real world with actual objects and processes, how can we separate robustly real biological characters from uncritically reified characters? One way to avoid reification is through the employment of objectivity criteria that give us good methods for identifying robust primary homology statements. I identify six such criteria and explore (...) each with examples. Ultimately, it is important to minimize character reification, because poor character analysis leads to dismal cladograms, even when proper phylogenetic analysis is employed. Given the deep and systemic problems associated with character reification, it is ironic that philosophers have focused almost entirely on phylogenetic analysis and neglected character analysis. (shrink)

This article explores the rise of comics-based research (CBR) as an innovative method for disseminating and translating academic findings to broader audiences. Rooted in the established use of comics in technical communication, CBR takes the unique strengths of graphic media—accessibility, multimodal engagement, and visual storytelling—to communicate complex concepts to diverse audiences, particularly in health-related disciplines. A recent development in this field is the comic research abstract, a concise, visually enriched alternative to traditional textual abstracts. By integrating clarity, brevity, and (...) expressive visuals, this format enhances research accessibility and promotes interdisciplinary collaboration. Drawing on an example from the author’s work on intergenerational storytelling, this article introduces the comic research abstract as a transformative interdisciplinary tool that bridges the arts, humanities, and health sciences. It highlights how this format translates research into advocacy-driven narratives, fostering inclusion, activism, and public engagement. By combining written and visual content, the comic research abstract underscores the potential of comics for advancing health humanities, arts-based academic communication, and inclusive scholarship. (shrink)

In addition to their core explanatory and predictive assumptions, scientific models include simplifying assumptions, which function as idealizations, approximations, and abstractions. There are methods to investigate whether simplifying assumptions bias the results of models, such as robustness analyses. However, the equally important issue – the focus of this paper – has received less attention, namely, what are the methodological and epistemic strengths and limitations associated with different simplifying assumptions. I concentrate on one type of simplifying assumption, the use of mega (...) parameters as abstractions in ecological models. First, I argue that there are two kinds of mega parameters qua abstractions, sufficient parameters and aggregative parameters, which have gone unnoticed in the literature. The two are associated with different heuristics, holism and reductionism, which many view as incompatible. Second, I will provide a different analysis of abstractions and the associated heuristics than previous authors. Reductionism and holism and the accompanying abstractions have different methodological and epistemic functions, strengths, and limitations, and the heuristics should be viewed as providing complementary research perspectives of cognitively limited beings. This is then, third, used as a premise to argue for epistemic and methodological pluralism in theoretical ecology. Finally, the presented taxonomy of abstractions is used to comment on the current debate whether mechanistic accounts of explanation are compatible with the use of abstractions. This debate has suffered from an abstract discussion of abstractions. With a better taxonomy of abstractions the debate can be resolved. (shrink)

A new case of Shelah's eventual categoricity conjecture is established: Let be an abstract elementary class with amalgamation. Write and. Assume that is H2‐tame and has primes over sets of the form. If is categorical in some, then is categorical in all. The result had previously been established when the stronger locality assumptions of full tameness and shortness are also required. An application of the method of proof of the mentioned result is that Shelah's categoricity conjecture holds in the (...) context of homogeneous model theory (this was known, but our proof gives new cases): If D be a homogeneous diagram in a first‐order theory T and D is categorical in a, then D is categorical in all. (shrink)

Beyond the Senses, Abstraction - At the center of this study are three nonmimetic examples: a twelfth-century cloister pillar, a thirteenth-century reliquary, and a fourteenth-century manuscript illumination. These nonfigurative objects, representing three media and spanning three centuries, show that abstraction - predicated as it was on the theological articulation between truth, facts, and language - emerged in the Middle Ages as the primary vehicle for materializing the ineffable. The analysis begins by considering medieval notions of abstraction as (...) a mode of figuration. It goes on to demonstrate how the abstractive operations at work in these images, each in a distinctive visual method, encouraged the pursuit of truth that lies beyond sensory perception by engendering the process of abstraction as it was understood in the Middle Ages: that of withdrawal, removal, paring down. This subtractive process, both visual and intellectual, allowed the beholder to reach through the perceptible and the graspable, and thus to apprehend what is most emphatically unavailable to the senses. (shrink)

Monsieur Schouls a établi un certain nombre de points, avec lesquels je me declarerai d'accord. Je crois qu'il a raison d'affirmrr que pour Locke, le fondement de toute connaissance au niveau initial de l'expérience est un divers de la sensation ou de la réflexion formé par des combinations d'idées unies ensemble. D'autre part, la description de la maniere dont l'esprit acquiert la connaissance générale par un processus d'abstraction et done d'analyse me semble conforme à l'épistémologie de Locke.Mais je crois (...) que par ce processus, l'esprit atteint seulement le niveau de la connaissance générale; la connaissance générale elle-même consiste dans la démonstration et, meme si la démonstration se raméné à une chaîne d'intuitions, conformément au modèle cartésien des Regulae, c'est seulement dans l'illatio que l'on peut situer ce que M. Schouls qualifie de synthèse: c'est cette illatio qui constitue proprement la science.D'où le problème de cette éthique démontrable dont il faudrait établir, conformément à cette thèse, le mode de formation “synthétique” à partir d'axiomes et de principes. (shrink)