The results of applying Soft Systems Methodology (SSM) show that the nature of the solution and improvement in the problem situation involves some ambiguity. This is due to SSM’s theoretical inadequacy in extending multiple conceptual models to an agreed-upon human activity system. In fact, one of the most important and controversial issues in soft operations research is to ensure how the solution has been obtained and to secure whether the conditions under which the solution has been obtained were (...) satisfied. This article presents the necessary and sufficient conditions for achieving human activity systems as a solution to one of the widely-used methodologies of soft operations research, i.e. Soft Systems Methodology. Similarly, with the aim of reaching a better understanding of the nature of the solution provided by SSM, the soft solution is compared through an example with that of hard systems methodology. (shrink)

Necessary and sufficient conditions are presented for the (first-order) theory of a universal class of algebraic structures (algebras) to have a model completion, extending a characterization provided by Wheeler. For varieties of algebras that have equationally definable principal congruences and the compact intersection property, these conditions yield a more elegant characterization obtained (in a slightly more restricted setting) by Ghilardi and Zawadowski. Moreover, it is shown that under certain further assumptions on congruence lattices, the existence of (...) a model completion implies that the variety has equationally definable principal congruences. This result is then used to provide necessary and sufficient conditions for the existence of a model completion for theories of Hamiltonian varieties of pointed residuated lattices, a broad family of varieties that includes lattice-ordered abelian groups and MV-algebras. Notably, if the theory of a Hamiltonian variety of pointed residuated lattices has a model completion, it must have equationally definable principal congruences. In particular, the theories of lattice-ordered abelian groups and MV-algebras do not have a model completion, as first proved by Glass and Pierce, and Lacava, respectively. Finally, it is shown that certain varieties of pointed residuated lattices generated by their linearly ordered members, including lattice-ordered abelian groups and MV-algebras, can be extended with a binary operation to obtain theories that do have a model completion. (shrink)

This contribution aims at providing an argumentative method to account for epistemic modality and evidentiality. I claim that these two linguistic categories can work as semantic components of defeasible argumentative schemes based on classification processes. This kind of approximate reasoning is, in fact, frequently indicated by appearance verbs which signal that the inferred standpoint is conceived by the speaker as uncertain due to the deceiving nature of perceptual data. Drawing from an analysis at the semantic-argumentative interface, the way in which (...) prototype theory sheds light on the processes of meaning construction underlying defeasible arguments from definition is also shown. (shrink)

The notion of scientific representation plays a central role in current debates on modeling in the sciences. One or maybe the major epistemic virtue of successful models is their capacity to adequately represent specific phenomena or target systems. According to similarity views of scientific representation, models should be similar to their corresponding targets in order to represent them. In this paper, Suárez’s arguments against similarity views of representation will be scrutinized. The upshot is that the intuition that scientific (...) representation involves similarity is not refuted by the arguments. The arguments do not make the case for the strong claim that similarity between vehicles and targets is neither necessary nor sufficient for scientific representation. Especially, one claim that a similarity view wants to uphold, still, is the following thesis: only if a vehicle is similar to a target in relevant respects and to a specific degree of similarity then the vehicle is a scientific representation of that target. (shrink)

In this article the standard philosophical method involving intuition-driven conceptual analysis is challenged in a new way. This orthodox approach to philosophy takes analysanda to be the specifications of the content of concepts in the form of sets of necessary and sufficient conditions. Here it is argued that there is no adequate account of what necessary and sufficient conditions are. So, the targets of applications of the standard philosophical method so understood are not sufficiently (...) well understood for this method to be dependable. (shrink)

A theory of necessary and sufficient conditions is presented, as well as a theory of necessary and sufficient causes and effects, viewed as a particular case of the former. Ambiguities of the terms 'condition' and 'necessary condition' are explored, and a neutral meaning for 'condition' is favoured. The relation between necessary and sufficient conditions and implicative conditionals (including counterfactuals) is also discussed. Two problems of counterfactual theories of causal explanation are indicated, (...) concerning (i) how to account for causes that are not necessary and (ii) how to interpret the counterfactual from the negation of the effect to the negation of the cause. Application of the theory of necessary and sufficient conditions to Euler’s explanation of the Königsberg bridge problem is discussed. The theory of necessary and sufficient causes and effects is then applied to the flagpole shadow explanation and to two biological explanations, one involving a sufficient but not necessary cause and the other a necessary but not sufficient cause. Causes that are neither sufficient nor necessary are also recognized. Finally, a probabilistic approach to causes that are either not sufficient or not necessary is explored, including its application to examples of such cases. (shrink)

We present a necessary and sufficient condition for the embeddability of a principally decomposable finite lattice into the computably enumerable degrees. This improves a previous result which required that, in addition, the lattice be ranked. The same condition is also necessary and sufficient for a finite lattice to be embeddable below every non-zero computably enumerable degree.

Describes the received theory of necessary and sufficient conditions, explains some standard objections to it, and lays out alternative ways of thinking about conditions and conditionals.

Claims that necessary and sufficient conditions are not converse relations are discussed, as well as the related claim that If A, then B is not equivalent to A only if B . The analysis of alleged counterexamples has shown, among other things, how necessary and sufficient conditions should be understood, especially in the case of causal conditions, and the importance of distinguishing sufficient-cause conditionals from necessary-cause conditionals. It is concluded that (...) class='Hi'>necessary and sufficient conditions, adequately interpreted, are converse relations in all cases. (shrink)

We define a class of finite partial lattices which admit a notion of rank compatible with embedding constructions, and present a necessary and sufficient condition for the embeddability of a finite ranked partial lattice into the computably enumerable degrees.

We present a necessary and sufficient condition for the embeddability of a finite principally decomposable lattice into the computably enumerable degrees preserving greatest element.

This chapter introduces and discusses the concepts of necessary and sufficient conditions.

There is a variety of concepts of the divine in the eastern and western theological and philosophical traditions. There is, however, not enough reflection on the logic behind concepts of God and their justification. I clarify some necessary and sufficient conditions any attempt to explicate a concept of God has to take into account. I argue that each concept of God is a cypher for a particular worldview and distinguishes three types of justification frequently used to bestow (...) content on particular concepts of God: philosophical, theological, and scientific. I turn to four fundamental models of the God–world relation and argue that the most promising concept of God is panentheistic, on which the universe is essentially divine but is not exhaustive of the divine being. (shrink)

Scoring rules measure the deviation between a forecast, which assigns degrees of confidence to various events, and reality. Strictly proper scoring rules have the property that for any forecast, the mathematical expectation of the score of a forecast p by the lights of p is strictly better than the mathematical expectation of any other forecast q by the lights of p. Forecasts need not satisfy the axioms of the probability calculus, but Predd et al. [9] have shown that given a (...) finite sample space and any strictly proper additive and continuous scoring rule, the score for any forecast that does not satisfy the axioms of probability is strictly dominated by the score for some probabilistically consistent forecast. Recently, this result has been extended to non-additive continuous scoring rules. In this paper, a condition weaker than continuity is given that suffices for the result, and the condition is proved to be optimal. (shrink)

It would be very desirable to have an account of the relation between mind and world that sustained the integrity of each. In this paper, we will argue that a theory of cognition which is broadly Thomistic can do just that. Many commentators recognize that cognitio is Aquinas’s basic epistemic concept, and that it designates knowledge in the broadest and most basic sense, as distinguished from scientia, or knowledge in the paradigmatic sense. There are several important consequences of this distinction (...) which are relevant to a proper understanding of the way in which a theory of knowledge which is in the Aristotelian-Thomistic tradition approaches the issue of the relation between the mind and the world. First and foremost, knowledge cannot be construed as a univocal concept in the A/t context. There are different senses of knowledge and we should not expect there to be a theory which supplies necessary and sufficient conditions for “S knows that p” that satisfies all the different senses of knowledge. It is perplexing that the contemporary discussion seems to miss this point, for the same sort of systematic ambiguity of the term ‘knowledge’ seems to hold in English. Second, the A/t theory of knowledge is not an epistemological theory in the modern sense, if by “epistemological” we mean one which is clearly demarcated from a metaphysical, psychological, or even semantical theory. The A/t theory is a metaphysics of knowledge. Third, a Thomistic theory of knowledge begins with a theory of cognition which provides the grounds of knowledge across the board, including even that of scientia. (shrink)

In this paper, we consider choice functions that are unanimous, anonymous, symmetric, and group strategy-proof and consider domains that are single-peaked on some tree. We prove the following three results in this setting. First, there exists a unanimous, anonymous, symmetric, and group strategy-proof choice function on a path-connected domain if and only if the domain is single-peaked on a tree and the number of agents is odd. Second, a choice function is unanimous, anonymous, symmetric, and group strategy-proof on a single-peaked (...) domain on a tree if and only if it is the pairwise majority rule and the number of agents is odd. Third, there exists a unanimous, anonymous, symmetric, and strategy-proof choice function on a strongly path-connected domain if and only if the domain is single-peaked on a tree and the number of agents is odd. As a corollary of these results, we obtain that there exists no unanimous, anonymous, symmetric, and group strategy-proof choice function on a path-connected domain if the number of agents is even. (shrink)

Jeffrey updating is a natural extension of Bayesian updating to cases where the evidence is uncertain. But, the resulting degrees of belief appear to be sensitive to the order in which the uncertain evidence is acquired, a rather un-Bayesian looking effect. This order dependence results from the way in which basic Jeffrey updating is usually extended to sequences of updates. The usual extension seems very natural, but there are other plausible ways to extend Bayesian updating that maintain order-independence. I will (...) explore three models of sequential updating, the usual extension and two alternatives. I will show that the alternative updating schemes derive from extensions of the usual rigidity requirement, which is at the heart of Jeffrey updating. Finally, I will establish necessary and sufficient conditions for order-independent updating, and show that extended rigidity is closely related to these conditions. (shrink)

I elaborate on Pylyshyn's definition of the cognitive impenetrability (CI) of early vision, and draw on the role of concepts in perceptual processing, which links the problem of the CI or cognitive penetrability (CP) of early vision with the problem of the nonconceptual content (NCC) of perception. I explain, first, the sense in which the content of early vision is CI and I argue that if some content is CI, it is conceptually encapsulated, that is, it is NCC. Then, I (...) examine the definitions of NCC and argue that they lead to the view that the NCC of perception is retrieved in a stage of visual processing that is CI. Thus, the CI of a state and content is a sufficient and necessary condition for the state and its content to be purely NCC, the CI?≡?NCC thesis. Since early vision is CI, the purely NCC of perception is formed in early vision. I defend the CI?≡?NCC thesis by arguing against objections raised against both the sufficient and the necessary part of the thesis. (shrink)

What role do demand deposits serve in the financial system? The answer to this simple question has great implications in keeping the legal terms of the contract consistent with the demands of the financial system. Demand deposits are a perfect monetary substitute. Since money is only held to hedge against perceived uncertainty in both the timing and magnitude of future expenditures, demand deposits are demanded for the same reason. From this we derive three main conclusions. First, a financial contract similar (...) to a demand deposit cannot substitute for money. Second, full agreement to a financial contract does not create a perfect substitute for money unless it provides money’s two key characteristics: on demand and par value redemption. Finally, the demand for fractional-reserve demand deposits is fostered by an exogenous source and that demand for a good or service is not a sufficient condition to justify its legality or ethicality. (shrink)

The paper proposes a minimal definition of dreaming in terms of immersive spatiotemporal hallucination (ISTH) occurring in sleep or during sleep–wake transitions and under the assumption of reportability. I take these conditions to be both necessary and sufficient for dreaming to arise. While empirical research results may, in the future, allow for an extension of the concept of dreaming beyond sleep and possibly even independently of reportability, ISTH is part of any possible extension of this definition and (...) thus is a constitutive condition of dreaming. I also argue that the proposed ISTH model of dreaming, in conjunction with considerations on the epistemic relationship between dreaming and dream reports, raises important questions about the extent to which dreams typically involve a detailed body representation—an assumption that plays an important role in philosophical work on dreaming. As a commonly accepted definition of dreaming is lacking in current dream research, the ISTH model, which integrates conceptual analysis and epistemological considerations with results from empirical research, is an important contribution to this field. By linking dreaming to felt presence, full-body illusions, and autoscopic phenomena such as out-of-body experiences in wakefulness and in the hypnagogic state, the ISTH model of dreaming also helps integrate dream research, both theoretically and experimentally, with the study of other altered states of consciousness involving hallucinations. It makes straightforward and investigable predictions by claiming that all of these experiences have amodal spatiotemporal hallucinations as their common denominator. Finally, it is theoretically relevant for the philosophical discussion on minimal phenomenal selfhood. (shrink)

Iris Marion Young presents a social connection model on which those, and only those, who participate in structural processes that produce injustice have a forward-looking responsibility to redress the resulting injustice by challenging the structures that produce it. In Young's view, this is an all-things-considered, albeit discretionary, responsibility. I argue that participation in a structural process that produces injustice is neither necessary nor sufficient for having political responsibilities, and that therefore the social connection model must be rejected. A (...) subtler model is needed, one that depicts participation in a structural process that produces injustice as sufficient for having pro tanto forward-looking responsibilities to redress the process, unless the participating agent satisfies certain excusing conditions. I suggest the intuitive force of the thought that mere participation gives us political responsibilities can be explained by more fundamental considerations. Hastily, we might conclude that all participants have political responsibilities simply because most of them satisfy at least one of the following conditions: they cause injustice to continue, they are morally responsible for injustice, they benefit from injustice, they have communal ties with the victims of injustice, or they have the capacity to redress injustice. (shrink)

Drawing on the historical insight of Emer de Vattel to build on the contemporary arguments of Michael Walzer and David Luban, this article develops a model of sufficient risk as a necessary condition for anticipatory war to be deemed self-defence. This model holds that an anticipatory war may constitute legitimate self-defence (as opposed to aggression) when it aims to forestall a threat that poses a sufficient risk to the anticipating state. This is the point where a threat (...) is both sufficiently likely to materialise and sufficiently large to pose a grave risk. Due to crucial problems with the imminence condition for self-defence, I propose that the sufficient risk condition subsume that of imminence. The power of this model lies in its ability to encapsulate all factors raised by previous authors that are morally relevant specifically for anticipatory wars and categorise them as contributing to the judgement of the likelihood of the threat materialising and/or the magnitude of the potential threat. This parsimonious categorisation increases the accuracy and clarity of the moral theory on anticipatory war, making it more robust to change in the types of threats faced by states, and less ripe for manipulation to justify immoral wars. (shrink)

Both biologists and philosophers often make use of simple verbal formulations of necessary and sufficient conditions for evolution by natural selection (ENS). Such summaries go back to Darwin's Origin of Species (especially the "Recapitulation"), but recent ones are more compact.1 Perhaps the most commonly cited formulation is due to Lewontin.2 These summaries tend to have three or four conditions, where the core requirement is a combination of variation, heredity, and fitness differences. The summaries are employed in (...) several ways. First, they are often used in pedagogical contexts, and in showing the coherence of evolutionary theory in response to attacks from outside biology. Second, they are important in discussions of extensions of evolutionary principles to new domains, such as cultural change. The summaries also have intrinsic scientific and philosophical interest as attempts to capture some core principles of evolutionary theory in a highly concise way. Despite their prominence, both the proper formulation and status of these summaries are unclear. Standard formulations are subject to counterexamples, and their relations to formal models of evolutionary change are not straightforward. Here I look closely at these verbal summaries, and at how they relate to formal models. Are the summaries merely rough approximations that have no theoretical role of their own? Perhaps they could operate as theoretical statements in Darwin's time, but have now been superseded by more exact treatments. (shrink)

The ability of predicting upcoming events or conditions in advance offers substantial selective advantage to living beings. The most successful systematic tool for fairly reliable prognoses is the use of dynamical causal models in combination with memorised experience. Surprisingly, causality is a fundamental but rather controversially disputed concept. For both models and memory, symbol processing is requisite. Symbols are a necessary and sufficient attribute of life from its very beginning; the process of their evolutionary emergence (...) was discovered by Julian Huxley a century ago. In behavioural biology, this universal symmetry-breaking kinetic phase transition became known as ritualisation. Symbol use for predicting future dynamical processes has culminated in the unprecedented complexity of mental models used in science and technology, coining the historical ascent of modern humans. Observation and measurement transform structural information of physical exchange processes into symbolic information from which state quantities are derived by means of mental models. However, phylogenetically inherited models such as naïve realism do not necessarily explain the sophisticated insights revealed by modern experiments with, say, entangled quantum states. It is suggested to carefully distinguish observed exchange quantities from predicted unobservable state quantities, and physical reality from mental models thereof. (shrink)

New Caledonian crow populations have developed complex tools that show suggestive evidence of cumulative change. These tool designs, therefore, appear to be the product of cumulative technological culture. We suggest that tool-using NC crows offer highly useful data for current debates over the necessary and sufficient conditions for the emergence of CTC.

I model sequential decisions over multiple interconnected propositions and investigate path-dependence in such decisions. The propositions and their interconnections are represented in propositional logic. A sequential decision process is path-dependent if its outcome depends on the order in which the propositions are considered. Assuming that earlier decisions constrain later ones, I prove three main results: First, certain rationality violations by the decision-making agent—individual or group—are necessary and sufficient for path-dependence. Second, under some conditions, path-dependence is unavoidable in (...) decisions made by groups. Third, path-dependence makes decisions vulnerable to strategic agenda setting and strategic voting. I also discuss escape routes from path-dependence. My results are relevant to discussions on collective consistency and reason-based decision-making, focusing not only on outcomes, but also on underlying reasons, beliefs, and constraints. (shrink)

Outlines the core of the author's theory, according to which the concept of knowledge arises because of our interest in having true beliefs about our environment and thus in evaluating sources of information, and is used to flag approved ones. The hypothesis is used to account for epistemologists’ disagreement over the precise nature of the belief condition for knowledge. Ground is conceded to those who play down the requirement, in so far as an informant's being confident that p is not (...) always taken as necessary for her to be a good informant. Equally, cases in which an informant is regarded as good, yet lacks belief entirely, are freakish and thus of little practical use, which explains both the attraction of the requirement and the feeling that there are genuine counter‐examples to it. (shrink)

In this paper, two different axiologies of pleasure are attributed to Hutcheson and Mill. Hutcheson endorsed a hedonist axiology, where quality of pleasure works as a still quantitative factor, able to counterbalance other quantitative features of pleasurable mental states - such as intensity and duration. By contrast, in Mill's view of value, the quality of pleasures is the only value-making feature, silencing any contribution from other quantitative elements. Therefore, the presence of certain qualitative characteristics - namely, the connection of certain (...) pleasures with human active faculties - becomes a necessary and sufficient condition of value. Due to this unique role of quality, Mill's axiology opens the way to non-pleasurable experiences being valuable - for non-pleasurable exercises of the human active faculties meet the condition to be valuable states. Thus, Mill's theory of value is declared non-hedonistic - against the recent claims to the contrary put forth by W. Donner. (shrink)

The Trek Separation Theorem states necessary and sufficient conditions for a linear directed acyclic graphical model to entail for all possible values of its linear coefficients that the rank of various sub-matrices of the covariance matrix is less than or equal to n, for any given n. In this paper, I extend the Trek Separation Theorem in two ways: I prove that the same necessary and sufficient conditions apply even when the generating model is (...) partially non-linear and contains some cycles. This justifies application of constraint-based causal search algorithms to data generated by a wider class of causal models that may contain non-linear and cyclic relations among the latent variables. (shrink)

There exist two known types of ultrafilter extensions of first-order models, both in a certain sense canonical. One of them comes from modal logic and universal algebra, and in fact goes back to Jónsson and Tarski :891–939, 1951; 74:127–162, 1952). Another one The infinity project proceeding, Barcelona, 2012) comes from model theory and algebra of ultrafilters, with ultrafilter extensions of semigroups as its main precursor. By a classical fact of general topology, the space of ultrafilters over a discrete space (...) is its largest compactification. The main result of Saveliev The infinity project proceeding, Barcelona, 2012), which confirms a canonicity of this extension, generalizes this fact to discrete spaces endowed with an arbitrary first-order structure. An analogous result for the former type of ultrafilter extensions was obtained in Saveliev. Results of such kind are referred to as extension theorems. After a brief introduction, we offer a uniform approach to both types of extensions based on the idea to extend the extension procedure itself. We propose a generalization of the standard concept of first-order interpretations in which functional and relational symbols are interpreted rather by ultrafilters over sets of functions and relations than by functions and relations themselves, and define ultrafilter models with an appropriate semantics for them. We provide two specific operations which turn ultrafilter models into ordinary models, establish necessary and sufficient conditions under which the latter are the two canonical ultrafilter extensions of some ordinary models, and obtain a topological characterization of ultrafilter models. We generalize a restricted version of the extension theorem to ultrafilter models. To formulate the full version, we propose a wider concept of ultrafilter models with their semantics based on limits of ultrafilters, and show that the former concept can be identified, in a certain way, with a particular case of the latter; moreover, the new concept absorbs the ordinary concept of models. We provide two more specific operations which turn ultrafilter models in the narrow sense into ones in the wide sense, and establish necessary and sufficient conditions under which ultrafilter models in the wide sense are the images of ones in the narrow sense under these operations, and also are two canonical ultrafilter extensions of some ordinary models. Finally, we establish three full versions of the extension theorem for ultrafilter models in the wide sense. The results of the first three sections of this paper were partially announced in Poliakov and Saveliev On two concepts of ultrafilter extensions of first-order models and their generalizations, Springer, Berlin, 2017). (shrink)

This paper provides a unifying axiomatic account of the interpretation of recursive types that incorporates both domain-theoretic and realizability models as concrete instances. Our approach is to view such models as full subcategories of categorical models of intuitionistic set theory. It is shown that the existence of solutions to recursive domain equations depends upon the strength of the set theory. We observe that the internal set theory of an elementary topos is not strong enough to guarantee their (...) existence. In contrast, as our first main result, we establish that solutions to recursive domain equations do exist when the category of sets is a model of full intuitionistic Zermelo–Fraenkel set theory. We then apply this result to obtain a denotational interpretation of FPC, a recursively typed lambda-calculus with call-by-value operational semantics. By exploiting the intuitionistic logic of the ambient model of intuitionistic set theory, we analyse the relationship between operational and denotational semantics. We first prove an “internal” computational adequacy theorem: the model always believes that the operational and denotational notions of termination agree. This allows us to identify, as our second main result, a necessary and sufficient condition for genuine “external” computational adequacy to hold, i.e. for the operational and denotational notions of termination to coincide in the real world. The condition is formulated as a simple property of the internal logic, related to the logical notion of 1-consistency. We provide useful sufficient conditions for establishing that the logical property holds in practice. Finally, we outline how the methods of the paper may be applied to concrete models of FPC. In doing so, we obtain computational adequacy results for an extensive range of realizability and domain-theoretic models. (shrink)

In recent years, the fight against money laundering has emerged as a key issue of financial regulation. The Wolfsberg Group is an important multistakeholder agreement establishing corporate responsibility principles against money laundering in a domain where international coordination remains otherwise difficult. The fact that 10 out of the 25 top private banking institutions joined this initiative opens up an interesting puzzle concerning the conditions for the participation of key industry players in the Wolfsberg Group. The article presents a fuzzy-set (...) analysis of seven hypotheses based on firm-level organizational factors, the macro-institutional context, and the regulatory framework. Results from the analysis of these 25 financial institutions show that public ownership of the bank and the existence of a code of conduct are necessary conditions for participation in the Wolfsberg Group, whereas factors related to the type of financial institution, combined with the existence of a black list, are sufficient for explaining participation. (shrink)

Under some assumptions on an equational theory S , we give a necessary and sufficient condition so that S admits a model completion. These assumptions are often met by the equational theories arising from logic. They say that the dual of the category of finitely presented S-algebras has some categorical stucture. The results of this paper combined with those of [7] show that all the 8 theories of amalgamable varieties of Heyting algebras [12] admit a model completion. Further (...) applications to varieties of modal algebras are given in [8]. (shrink)

We prove that a necessary and sufficient condition for a countable set L of sets of integers to be equal to the algebra of all sets of integers definable in a nonstandard elementary extension of ω by a formula of the PA language which may include the standardness predicate but does not contain nonstandard parameters, is as follows: L is closed under arithmetical definability and contains 0 (ω) , the set of all (Gödel numbers of) true arithmetical sentences. (...) Some results related to definability of sets of integers in elementary extensions of ω are included. (shrink)

Originally a keynote address at the International Society for Research on Emotion (ISRE) 2013 convention, this article surveys many nonobvious ways that emotion phenomena show up in natural language. One conclusion is that no classical Aristotelian definition of “emotion” in terms of necessary and sufficient conditions is possible. The brain naturally creates radial, not classical categories. As a result, “emotion” is a contested concept. There is no one correct, classical definition of “emotion.” There are real emotion (...) phenomena that can be precisely studied, and language is an important area to look at for such phenomena. (shrink)

We show that the quantifier elimination result for the Shelah-Spencer almost sure theories of sparse random graphs $$G(n,n^{-\alpha })$$ given by Laskowski (Isr J Math 161:157–186, 2007) extends to their various analogues. The analogues will be obtained as theories of generic structures of certain classes of finite structures with a notion of strong substructure induced by rank functions and we will call the generics Baldwin–Shi hypergraphs. In the process we give a method of constructing extensions whose ‘relative rank’ is negative (...) but arbitrarily small in context. We give a necessary and sufficient condition for the theory of a Baldwin–Shi hypergraph to have atomic models. We further show that for certain well behaved classes of theories of Baldwin–Shi hypergraphs, the existentially closed models and the atomic models correspond. (shrink)

This essay gives necessary and sufficient conditions for recovering expected utility from choice behavior in several popular models of uncertainty. In particular, these techniques handle a finite state model; a model for which the choice space consists of probability densities and the expected utility representation requires bounded, measurable utility; and a model for which the choice space consists of Borel probability measures and the expected utility representation requires bounded, continuous utility. The key result is the identification (...) of the continuity condition necessary for the revelation of linear utility. (shrink)

Let $\sigma$ denote the number of automorphisms of a model $\mathfrak{U}$ of power $\omega_1$. We derive a necessary and sufficient condition in terms of trees for the existence of an $\mathfrak{U}$ with $\omega_1 < \sigma < 2^{\omega_1}$. We study the sufficiency of some conditions for $\sigma = 2^{\omega_1}$. These conditions are analogous to conditions studied by D. Kueker in connection with countable models.

Let σ(U) denote the number of automorphisms of a model U of power ω1. We derive a necessary and sufficient condition in terms of trees for the existence of an U with $\omega_1 < \sigma(\mathfrak{U}) < 2^{\omega_1}$. We study the sufficiency of some conditions for σ(U) = 2ω1 . These conditions are analogous to conditions studied by D. Kueker in connection with countable models.

The controversy about intentional explanation of action concerns how these explanations work. What kind of model allows us to capture the dependency or relevance relation between the explanans, i.e. the beliefs and desires of the agent, and the explanandum, i.e. the action? In this paper, I argue that the causal mechanical model can do the job. Causal mechanical intentional explanations consist in a reference to the mechanisms of practical reasoning of the agent that motivated the agent to act, i.e. to (...) a causally relevant set of beliefs and desires. Moreover, the causal mechanical model can provide in efficient and unproblematic applications, unlike action explanations using ceteris paribus laws or counterfactuals. The drawback of the latter models of explanation is their modal requirement: the explanans must mention or implies sufficient and/or necessary conditions for the explanandum. Such a requirement is too strong when it comes to intentional explanation of action. (shrink)

Definition: A condition A is said to be sufficient for a condition B, if (and only if) the truth (/existence /occurrence) [as the case may be] of A guarantees (or brings about) the truth (/existence /occurrence) of B.

In Swedish schools, the so-called ‘Participation Model’ is used to observe and analyse participation, with the intention of supporting an inclusive learning environment. While this model is widely promoted by government agencies, its theoretical alignment to the concept(s) of inclusion is not established. This article therefore compares and maps the six aspects of participation within the Participation Model (i.e. belonging, accessibility, interaction, autonomy, involvement and acceptance) with a hierarchically ordered set of commonly occuring definitions of inclusive education (ranging from the (...) lowest level, placement, to the highest, community). The Participation Model was found to provide necessary and sufficient conditions for the lower levels of inclusion, as well as necessary conditions for the higher levels of inclusion. However, we show that the model suffers from construct underrepresentation and outline a few possible solutions intended to increase the theoretical alignment between the Participation Model and the higher levels of inclusive education. Finally, we suggest directions for further research. (shrink)