We link two concepts from the literature, namely hard sequences for the satisfiability problem sat and so‐called pseudo proof systems proposed for study by Krajíček. Pseudo proof systems are elements of a particular nonstandard model constructed by forcing with random variables. We show that the existence of mad pseudo proof systems is equivalent to the existence of a randomized polynomial time procedure with a highly restrictive use of randomness which produces satisfiable formulas whose satisfying assignments are probably hard (...) to find. (shrink)

In the following we show that general property S considered by Cowen [1], Cowen and Kolany in [3] and earlier by Cowen in [2] and Kolany in [4] as hypergraph satisfiability, can be constructively reduced to (3, 2) · SAT , that is to satisfiability of (at most) triples with two-element forbidden sets. This is an analogue of the“classical” result on the reduction of SAT to 3 · SAT.

In this article, I argue that desire-satisfaction theories of well-being face the problem of trivially satisfied desires. First, I motivate the claim that desire-satisfaction theories need an aggregation principle and reconstruct four possible principles desire-satisfactionists can adopt. Second, I contend that one of these principles seems implausible on numerous counts. Third, I argue that the other three principles, which hold that the creation and satisfaction of new desires is good for individuals and can be called proliferationist, are vulnerable to (...) an objection from trivially satisfied desires. They implausibly imply that forming desires that are trivially satisfied is good for individuals. Finally, I argue that trivially satisfied desires may also worsen desire-satisfactionism's classical problem of pointless desires. Together, these claims constitute a challenge to desire-satisfactionism. (shrink)

I argue that George Schlesinger's proposed solution to the problem of evil fails because: (1) the degree of desirability of state of a being is not properly regarded as a trade‐off between happiness on the one hand and potential on the other; (2) degree of desirability of state is not capable of infinite increase; (3) there is no hierarchy of possible beings, but at most an ordering of such beings in terms of preferences; (4) the idea of such a (...) hierarchy is anyway morally repulsive. Schlesinger is right that the problem of evil disappears, but what makes it vanish is a recognition of the limits of our concepts of satisfaction and happiness, not the incoherent claim that satisfaction or happiness is capable of unlimited increase. (shrink)

We consider two‐variable, first‐order logic in which a single distinguished predicate is required to be interpreted as a transitive relation. We show that the finite satisfiability problem for this logic is decidable in triply exponential non‐deterministic time. Complexity falls to doubly exponential non‐deterministic time if the transitive relation is constrained to be a partial order.

In first order logic without equality, but with arbitrary relations and functions the ∃*∀∃* class is the unique maximal solvable prefix class. We show that the satisfiability problem for this class is decidable in deterministic exponential time The result is established by a structural analysis of a particular infinite subset of the Herbrand universe and by a polynomial space bounded alternating procedure.

We consider several natural fragments of the alternating-time temporal logics ATL* and ATL with restrictions on the nesting between temporal operators and strategic quantifiers. We develop optimal decision procedures for satisfiability in these fragments, showing that they have much lower complexities than the full languages. In particular, we prove that the satisfiability problem for state formulae in the full `strategically flat' fragment of ATL* is PSPACE-complete, whereas the satisfiability problems in the flat fragments of ATL and (...) ATL$^{+}$ are $\Sigma^P_3$-complete. We note that the nesting hierarchies for fragments of ATL* collapse in terms of expressiveness above nesting depth 1, hence our results cover all such fragments with lower complexities. (shrink)

The tree-based data structure of -tree for propositional formulas is introduced in an improved and optimised form. The -trees allow a compact representation for negation normal forms as well as for a number of reduction strategies in order to consider only those occurrences of literals which are relevant for the satisfiability of the input formula. These reduction strategies are divided into two subsets (meaning- and satisfiability-preserving transformations) and can be used to decrease the size of a negation normal (...) form A at (at most) quadratic cost. The reduction strategies are aimed at decreasing the number of required branchings and, therefore, these strategies allow to limit the size of the search space for the SAT problem. (shrink)

The tree-based data structure of △-tree for propositional formulas is introduced in an improved and optimised form. The △-trees allow a compact representation for negation normal forms as well as for a number of reduction strategies in order to consider only those occurrences of literals which are relevant for the satisfiability of the input formula. These reduction strategies are divided into two subsets (meaning- and satisfiability-preserving transformations) and can be used to decrease the size of a negation normal (...) form A at (at most) quadratic cost. The reduction strategies are aimed at decreasing the number of required branchings and, therefore, these strategies allow to limit the size of the search space for the SAT problem. (shrink)

Propositional logic has been recognized throughout the centuries as one of the cornerstones of reasoning in philosophy and mathematics. Over time, its formalization into Boolean algebra was accompanied by the recognition that a wide range of combinatorial problems can be expressed as propositional satisfiability (SAT) problems. Because of this dual role, SAT developed into a mature, multi-faceted scientific discipline, and from the earliest days of computing a search was underway to discover how to solve SAT problems in an automated (...) fashion. This book, the Handbook of Satisfiability, is the second, updated and revised edition of the book first published in 2009 under the same name. The handbook aims to capture the full breadth and depth of SAT and to bring together significant progress and advances in automated solving. Topics covered span practical and theoretical research on SAT and its applications and include search algorithms, heuristics, analysis of algorithms, hard instances, randomized formulae, problem encodings, industrial applications, solvers, simplifiers, tools, case studies and empirical results. SAT is interpreted in a broad sense, so as well as propositional satisfiability, there are chapters covering the domain of quantified Boolean formulae (QBF), constraints programming techniques (CSP) for word-level problems and their propositional encoding, and satisfiability modulo theories (SMT). An extensive bibliography completes each chapter. This second edition of the handbook will be of interest to researchers, graduate students, final-year undergraduates, and practitioners using or contributing to SAT, and will provide both an inspiration and a rich resource for their work. Edmund Clarke, 2007 ACM Turing Award Recipient: "SAT solving is a key technology for 21st century computer science." Donald Knuth, 1974 ACM Turing Award Recipient: "SAT is evidently a killer app, because it is key to the solution of so many other problems." Stephen Cook, 1982 ACM Turing Award Recipient: "The SAT problem is at the core of arguably the most fundamental question in computer science: What makes a problem hard?". (shrink)

Collective impact cases are situations where people collectively bring about a morally significant outcome by each acting in a certain way, and yet each individual action seems to make no, or almost no difference to the outcome. Intuitively, the beneficial or harmful outcomes give individuals moral reason to act (or refrain from acting) in collective impact situations. However, if the individual action does not make a difference to the outcome, it is not clear what those moral reasons are. The (...) class='Hi'>problem of collective impact is the challenge of identifying such moral reasons. Julia Nefsky has presented an account of how an individual action can help without making a difference – call it the Helping Account – that claims to provide a general solution to the problem of collective impact while avoiding problems faced by previously suggested solutions. I present an internal critique of Nefsky’s work. First, I argue that, based on the problems that Nefsky has raised against previously suggested solutions, three success conditions for a general solution to the problem of collective impact can be formulated: The Weightiness condition, the Generalizability condition, and the Connectedness condition. Second, I argue that the Helping Account fails to satisfy the three success conditions, thereby failing, by Nefsky’s own standards, to provide a general solution to the problem. (shrink)

Perfectionism, the view that well-being is a matter of developing characteristically human capacities, has relatively few defenders in the literature, but plenty of critics. This paper defends perfectionism against some recent formulations of classic objections, namely, the objection that perfectionism ignores the relevance of pleasure or preference for well-being, and a sophisticated version of the ‘wrong properties’ objection, according to which the intuitive plausibility of the perfectionist ideal is threatened by an absence of theoretical pressure to accept putative wrong properties (...) cases. The paper argues these objections are unsuccessful, but introduce a new worry, the Deep Problem: Perfectionism fails to offer a satisfying foundational justification for why developing the human essence is valuable. The paper responds to the deep problem, ultimately arguing that it is a puzzle put to all theories of well-being to provide a justification for their normative significance. (shrink)

The still unsettled decision problem for the restricted purely universal formulae 0-formulae) of the first order set-theoretic language based over =, ∈ is discussed in relation with the adoption or rejection of the axiom of foundation. Assuming the axiom of foundation, the related finite set-satisfiability problem for the very significant subclass of the 0-formulae consisting of the formulae involving only nested variables of level 1 is proved to be semidecidable on the ground of a reflection property over (...) the hereditarily finite sets, and various extensions of this result are obtained. When variables are restricted to range only over sets, in universes with infinitely many urelements the set-satisfiability problem is shown to be solvable provided the axiom of foundation is assumed; if it is not, then the decidability of a related derivability problem still holds. That, in turn, suggests the alternative adoption of an antifoundation axiom under which the set-satisfiability problem is also solvable . Turning to set theory without urelements, assuming a form of Boffa's antifoundation axiom, the complement of the set-satisfiability problem for the full class of Δ0-formulae is shown to be semidecidable; a result that is known not to hold, for the set-satisfiability problem itself, even for a very restricted subclass of the Δ0-formulae. (shrink)

I take it that the following is a desideratum of our theories in the philosophy of mind. A theory in the philosophy of mind should help us better understand ourselves as agents and aid in our theorizing about the nature of action and agency. In this paper I discuss a strategy adopted by some defenders of nonreductive physicalism in response to the problem of causal exclusion. The strategy, which I refer to as “intralevelism,” relies on treating mental causation as (...) intra level mental to mental causation, rather than as involving any inter level mental to physical causation. I raise problems for intralevelist theories of mental causation that stem from action-theoretic considerations. Specifically, I focus on the failure of intralevelist proposals to account for the problem of basic causal deviance in the etiology of action. To the extent that intralevelism fails to make room for basic causal deviance, the strategy fails to satisfy the aforementioned desideratum, viz ., that our theories in the philosophy of mind should be of use in theorizing about action and agency. The upshot is that intralevelism is a less promising strategy for nonreductive physicalists than it appears at first glance. (shrink)

A famous result of Hausdorff states that a sphere with countably many points removed can be partitioned into three pieces A, B, C such that A is congruent to B, B is congruent to C, and A is congruent to B ∪ C; this result was the precursor of the Banach–Tarski paradox. Later, R. Robinson characterized the systems of congruences like this which could be realized by partitions of the sphere with rotations witnessing the congruences. The pieces involved were nonmeasurable. (...) In the present paper, we consider the problem of which systems of congruences can be satisfied using open subsets of the sphere ; of course, these open sets cannot form a partition of the sphere, but they can be required to cover "most of" the sphere in the sense that their union is dense. Various versions of the problem arise, depending on whether one uses all isometries of the sphere or restricts oneself to a free group of rotations, or whether one omits the requirement that the open sets have dense union, and so on. While some cases of these problems are solved by simple geometrical dissections, others involve complicated iterative constructions and/or results from the theory of free groups. Many interesting questions remain open. (shrink)

The -logic of Terwijn is a variant of first-order logic with the same syntax in which the models are equipped with probability measures and the quantifier is interpreted as ‘there exists a set A of a measure such that for each,...’. Previously, Kuyper and Terwijn proved that the general satisfiability and validity problems for this logic are, i) for rational, respectively -complete and -hard, and ii) for, respectively decidable and -complete. The adjective ‘general’ here means ‘uniformly over all languages’. (...) We extend these results in the scenario of finite models. In particular, we show that the problems of satisfiability and validity with respect to finite models in E-logic are, i) for rational, respectively -complete and -complete, and ii) for, respectively decidable and -complete. Although partial results toward the countable case are also achieved, the computability of E-logic over countable models still remains largely unsolved. In addition, most o... (shrink)

Contact Logics provide a natural framework for representing and reasoning about regions in several areas of computer science. In this paper, we focus our attention on reasoning methods for Contact Logics and address the satisfiability problem and the unifiability problem. Firstly, we give sound and complete tableaux-based decision procedures in Contact Logics and we obtain new results about the decidability/complexity of the satisfiability problem in these logics. Secondly, we address the computability of the unifiability (...) class='Hi'>problem in Contact Logics and we obtain new results about the unification type of the unifiability problem in these logics. (shrink)

The desire-satisfaction theory of welfare says, roughly, that one's life goes well to the extent that one's desires are satisfied. On standard 'actualist' versions of the theory, it doesn't matter what you desire. So long as you are getting what you actually want – whatever it is – things are going well for you. There is widespread agreement that these standard versions are incorrect, because we can desire things that are bad for us -– in other words, because there are (...) 'defective desires'. The aim of this paper is to defend the actualist desire-satisfaction theory against the problem of defective desires. I aim to show how the theory can accommodate the obvious fact that we can desire things that are bad for us. Admittedly, there are kinds of allegedly defective desire the theory cannot accommodate, but these desires, I argue, turn out not to be defective in the relevant way. (shrink)

In "Mathematical Truth", Paul Benacerraf articulated an epistemological problem for mathematical realism. His formulation of the problem relied on a causal theory of knowledge which is now widely rejected. But it is generally agreed that Benacerraf was onto a genuine problem for mathematical realism nevertheless. Hartry Field describes it as the problem of explaining the reliability of our mathematical beliefs, realistically construed. In this paper, I argue that the Benacerraf Problem cannot be made out. There (...) simply is no intelligible problem that satisfies all of the constraints which have been placed on the Benacerraf Problem. The point generalizes to all arguments with the structure of the Benacerraf Problem aimed at realism about a domain meeting certain conditions. Such arguments include so-called "Evolutionary Debunking Arguments" aimed at moral realism. I conclude with some suggestions about the relationship between the Benacerraf Problem and the Gettier Problem. (shrink)

There have been several different and even opposed conceptions of the problem of logical constants, i.e. of the requirements that a good theory of logical constants ought to satisfy. This paper is in the first place a survey of these conceptions and a critique of the theories they have given rise to. A second aim of the paper is to sketch some ideas about what a good theory would look like. A third aim is to draw from these ideas (...) and from the preceding survey the conclusion that most conceptions of the problem of logical constants involve requirements of a philosophically demanding nature which are probably not satisfiable by any minimally adequate theory. (shrink)

On Choice of Time Metric. What criteria ought to be satisfied by those observable processes which, accompanied by a function assigning values to intervals of that processes, serve as the standard for measurement of time? In how far do the criteria which can reasonably be established admit of an unambigous definition of time metric? That are the questions to which I have addressed myself in the paper. Peter Janich has aimed at solving the problem with careful avoidance of any (...) reference to physical theory. Although this paper owes a great deal to his ‘Protophysik der Zeit’, reasons will be ad-vanced that it is in principle impossible to give a foundation of time metric without any reference to physical theory. It follows that taking results of physical theory into account is unavoidable as far as a definite decision concerning the choice of time metric is aspired. At first sight reference to law-like assertions on the duration of temporal intervals appears to be paradoxical for it means to take something which originally ought to be submitted to experimental test as the standard for measurement. Poincaré is fairly conscious of this problem, yet explicitly acknowledges that there is a mutual relationship between definition of time metric and physical theory. It will be shown that this kind of mutual relationship which even might be termed as circular does not void physical theory of empirical content. Thus in the final part I am concerned to free the position which recommends reference to physical theory from its paradoxical image in order to advance a conventionalist account as a sceptical, but nevertheless fully satisfying solution. (shrink)

In its original form, Nozick’s experience machine serves as a potent counterexample to a simplistic form of hedonism. The pleasurable life offered by the experience machine, its seems safe to say, lacks the requisite depth that many of us find necessary to lead a genuinely worthwhile life. Among other things, the experience machine offers no opportunities to establish meaningful relationships, or to engage in long-term artistic, intellectual, or political projects that survive one’s death. This intuitive objection finds some support in (...) recent research regarding the psychological effects of phenomena such as video games or social media use. After a brief discussion of these problems, I will consider a variation of the experience machine in which many of these deficits are remedied. In particular, I’ll explore the consequences of a creating a virtual world populated with strongly intelligent AIs with whom users could interact, and that could be engineered to survive the user’s death. The presence of these agents would allow for the cultivation of morally significant relationships, and the world’s long-term persistence would help ground possibilities for a meaningful, purposeful life in a way that Nozick’s original experience machine could not. While the creation of such a world is obviously beyond the scope of current technology, it represents a natural extension of the existing virtual worlds provided by current video games, and it provides a plausible “ideal case” toward which future virtual worlds will move. While this improved experience machine would seem to represent progress over Nozick’s original, I will argue that it raises a number of new problems stemming from the fact that that the world was created to provide a maximally satisfying and meaningful life for the intended user. This, in turn, raises problems analogous in some ways to the problem(s) of evil faced by theists. In particular, I will suggest that it is precisely those features that would make a world most attractive to potential users—the fact that the AIs are genuinely moral agents whose well-being the user can significantly impact—that render its creation morally problematic, since they require that the AIs inhabiting the world be subject to unnecessary suffering. I will survey the main lines of response to the traditional problem of evil, and will argue that they are irrelevant to this modified case. I will close by considering by consider what constraints on the future creation of virtual worlds, if any, might serve to allay the concerns identified in the previous discussion. I will argue that, insofar as the creation of such worlds would allow us to meet morally valuable purposes that could not be easily met otherwise, we would be unwise to prohibit it altogether. However, if our processes of creation are to be justified, they must take account of the interests of the moral agents that would come to exist as the result of our world creation. (shrink)

We introduce the notion of “δ-complete decision procedures” for solving SMT problems over the real numbers, with the aim of handling a wide range of nonlinear functions including transcendental functions and solutions of Lipschitz-continuous ODEs. Given an SMT problemϕ and a positive rational number δ, a δ-complete decision procedure determines either that ϕ is unsatisfiable, or that the “δ-weakening” of ϕ is satisfiable. Here, the δ-weakening of ϕ is a variant of ϕ that allows δ-bounded numerical perturbations on ϕ. We (...) establish the existence and complexity of δ-complete decision procedures for bounded SMT over reals with functions mentioned above. We propose to use δ-completeness as an ideal requirement for numerically-driven decision procedures. As a concrete example, we formally analyze the DPLL〈ICP〉 framework, which integrates Interval Constraint Propagation in DPLL, and establish necessary and sufficient conditions for its δ-completeness. We discuss practical applications of δ-complete decision procedures for correctness-critical applications including formal verification and theorem proving. (shrink)

In the context of propositional logics, we apply semantics modulo satisfiability—a restricted semantics which comprehends only valuations that satisfy some specific set of formulas—with the aim to efficiently solve some computational tasks. Three possible such applications are developed.We begin by studying the possibility of implicitly representing rational McNaughton functions in Łukasiewicz Infinitely-valued Logic through semantics modulo satisfiability. We theoretically investigate some approaches to such representation concept, called representation modulo satisfiability, and describe a polynomial algorithm that builds representations (...) in the newly introduced system. An implementation of the algorithm, test results and ways to randomly generate rational McNaughton functions for testing are presented. Moreover, we propose an application of such representations to the formal verification of properties of neural networks by means of the reasoning framework of Łukasiewicz Infinitely-valued Logic.Then, we move to the investigation of the satisfiability of joint probabilistic assignments to formulas of Łukasiewicz Infinitely-valued Logic, which is known to be an NP-complete problem. We provide an exact decision algorithm derived from the combination of linear algebraic methods with semantics modulo satisfiability. Also, we provide an implementation for such algorithm for which the phenomenon of phase transition is empirically detected.Lastly, we study the game theory situation of observable games, which are games that are known to reach a Nash equilibrium, however, an external observer does not know what is the exact profile of actions that occur in a specific instance; thus, such observer assigns subjective probabilities to players actions. We study the decision problem of determining if a set of these probabilistic constraints is coherent by reducing it to the problems of satisfiability of probabilistic assignments to logical formulas both in Classical Propositional Logic and Łukasiewicz Infinitely-valued Logic depending on whether only pure equilibria or also mixed equilibria are allowed. Such reductions rely upon the properties of semantics modulo satisfiability. We provide complexity and algorithmic discussion for the coherence problem and, also, for the problem of computing maximal and minimal probabilistic constraints on actions that preserves coherence.prepared by Sandro Márcio da Silva Preto.E-mail: [email protected]:https://doi.org/10.11606/T.45.2021.tde-17062021-163257. (shrink)

There is a certain view abroad in the land concerning the philosophical problems raised by Tarskian semantics. This view has it that a Tarskian theory of truth in a language accomplishes nothing of interest beyond the definition of truth in terms of satisfaction, and, further, that what is missing — the only thing that would yield a solution to the philosophical problem of truth when added to Tarskian semantics — is a reduction of satisfaction to a non-semantic relation. It (...) seems to me that this view either misidentifies the philosophical problem altogether, or encourages a seriously misleading picture of the nature of the problem.The view I have in mind is nowhere more persuasively at work than in a recent paper by Hartry Field.1 In this paper Field argues that a Tarskian theory of truth for a natural language is impossible if we insist on Tarski's case-by-case elimination of ‘satisfies'. More fundamentally, however, he argues that a Tarskian theory could provide nothing of philosophical interest beyond the admittedly interesting reduction of truth to satisfaction, and his ground for this claim is, roughly, that a Tarskian theory does not reduce its primitive semantic relation — satisfaction — to a non-semantic relation. (shrink)

We identify the computational complexity of the satisfiability problem for FO 2 , the fragment of first-order logic consisting of all relational first-order sentences with at most two distinct variables. Although this fragment was shown to be decidable a long time ago, the computational complexity of its decision problem has not been pinpointed so far. In 1975 Mortimer proved that FO 2 has the finite-model property, which means that if an FO 2 -sentence is satisfiable, then it (...) has a finite model. Moreover, Mortimer showed that every satisfiable FO 2 -sentence has a model whose size is at most doubly exponential in the size of the sentence. In this paper, we improve Mortimer's bound by one exponential and show that every satisfiable FO 2 -sentence has a model whose size is at most exponential in the size of the sentence. As a consequence, we establish that the satisfiability problem for FO 2 is NEXPTIME-complete. (shrink)

This book constitutes the refereed proceedings of the 8th International Conference on Theory and Applications of Satisfiability Testing, SAT 2005, held in St Andrews, Scotland in June 2005. The 26 revised full papers presented together with 16 revised short papers presented as posters during the technical programme were carefully selected from 73 submissions. The whole spectrum of research in propositional and quantified Boolean formula satisfiability testing is covered including proof systems, search techniques, probabilistic analysis of algorithms and their (...) properties, problem encodings, industrial applications, specific tools, case studies, and empirical results. (shrink)

In days past, epistemologists expended a good deal of effort trying to analyze the basing relation—the relation between a belief and its basis. No satisfying account was offered, and the project was largely abandoned. Younger epistemologists, however, have begun to yearn for an adequate theory of basing. I aim to deliver one. After establishing some data and arguing that traditional accounts of basing are unsatisfying, I introduce a novel theory of the basing relation: the dispositional theory. It begins with the (...) pedestrian observation that beliefs stand or fall with their bases. The theory I offer is an elucidation and refinement of this thought. (shrink)

Ambivalence is most naturally characterized as a case of conflicting desires. In most cases, an agent’s intrinsic desires conflict contingently: there is some possible world in which both desires would be satisfied. This paper argues, though, that there are cases in which intrinsic desires necessarily conflict—i.e., the desires are not jointly satisfiable in any possible world. Desiring a challenge for its own sake is a paradigm case of such a desire. Ambivalence of this sort in an agent’s desires creates special (...) problems for the project of reducing all facts about an agent’s desires to facts about his or her preferences over options. If this reductive project fails, there is reason to suspect that the Decision Theory cannot give us a complete theory of Humean rationality. (shrink)

Duncan Pritchard has, in the years following his (2005) defence of a safety-based account of knowledge in Epistemic Luck, abjured his (2005) view that knowledge can be analysed exclusively in terms of a modal safety condition. He has since (Pritchard in Synthese 158:277–297, 2007; J Philosophic Res 34:33–45, 2009a, 2010) opted for an account according to which two distinct conditions function with equal importance and weight within an analysis of knowledge: an anti-luck condition (safety) and an ability condition-the latter being (...) a condition aimed at preserving what Pritchard now takes to be a fundamental insight about knowledge: that it arises from cognitive ability (Greco 2010; Sosa 2007, 2009). Pritchard calls his new view anti-luck virtue epistemology (ALVE). A key premise in Pritchard’s argument for ALVE is what I call the independence thesis; the thesis that satisfying neither the anti-luck condition nor the ability condition entails that the other is satisfied. Pritchard’s argument for the independence thesis relies crucially upon the case he makes for thinking that cognitive achievements are compatible with knowledge-undermining environmental luck—that is, the sort of luck widely thought to undermine knowledge in standard barn facade cases. In the first part of this paper, I outline the key steps in Pritchard’s argument for anti-luck virtue epistemology and highlight how it is that the compatibility of cognitive achievement and knowledge- undermining environmental luck is indispensible to the argument’s success. The second part of this paper aims to show that this compatibility premise crucial to Pritchard’s argument is incorrect. (shrink)

The Gettier problem concerns the definition of knowledge as justified true belief. In the paper I argue that Gettier's cases are not cases of justified true belief because Gettier's examples rely on some problematic assumptions. The first is rather elementary definition of justification and the other is that justification is preserved by entailment, that is, (A) for all agents X, if X is justified in believing that p , and X realizes that the truth of p entails the truth (...) of q , then X would also be justified in believing that q . For the simplistic conception of justification has some alarming consequences we pursue more adequate definition of justification which would satisfy the idea that a necessary condition of justification is to entail or to be entailed by a true proposition. We also show that the (A) is not necessary to provide an elegant counter-example to the definition of knowledge if the elementary definition of justification is adopted. (shrink)

The inference systems proposed for solving SAT are unsound for solving MaxSAT and MinSAT, because they preserve satisfiability but not the minimum and maximum number of clauses that can be falsified, respectively. To address this problem, we first define a clause tableau calculus for MaxSAT and prove its soundness and completeness. We then define a clause tableau calculus for MinSAT and also prove its soundness and completeness. Finally, we define a complete clause tableau calculus for solving both MaxSAT (...) and MinSAT, in that the minimum number of generated empty clauses provides an optimal MaxSAT solution and the maximum number provides an optimal MinSAT solution. (shrink)

Recall that [Formula: see text] is the lattice of Muchnik degrees of nonempty effectively compact sets in Euclidean space. We solve a long-standing open problem by proving that [Formula: see text] is dense, i.e. satisfies [Formula: see text]. Our proof combines an oracle construction with hyperarithmetical theory.

From electronic design problems to resolution proofs to SAT solvers, this book focuses on the satisfiabilityof theories that consist of propositional logic ...

I explain the shutdown problem: the problem of designing artificial agents that (1) shut down when a shutdown button is pressed, (2) don’t try to prevent or cause the pressing of the shutdown button, and (3) otherwise pursue goals competently. I prove three theorems that make the difficulty precise. These theorems show that agents satisfying some innocuous-seeming conditions will often try to prevent or cause the pressing of the shutdown button, even in cases where it’s costly to do (...) so. And patience trades off against shutdownability: the more patient an agent, the greater the costs that agent is willing to incur to manipulate the shutdown button. I end by noting that these theorems can guide our search for solutions. (shrink)

Until recently it has been conventional to assume that ethical egoism is "ethical" is name, alone, and that no account that considers one's own interests as the standard of moral obligation could count as seriously "ethical." In recent years, however, philosophers have shown increasing respect for more sophisticated forms of ethical egoism which attempt to define self-interest in enriched terms characterizing self-interest as human flourishing in both material and psychological dimensions. But philosophers are still skeptical that any conception of self-interest (...) could underpin ethical theory. This paper considers recent arguments by Richard Joyce, who is willing to concede enriched conceptions of self-interest, but who claims that egoism cannot support appropriate counterfactual conditionals about morality, or inferential uses of ordinary moral thinking. I argue that ethical egoism can satisfy each of Joyce's desiderata for morality, provided that it is taken to involve the very notion of enriched self-interest that Joyce is elsewhere willing to consider. In showing that egoism can count as a moral theory, I show, in effect, that Joyce's arguments for error theory about morality are really arguments for error theory about agent-neutral, non-egoistic morality. (shrink)

Even though the strong relationship between proof-theoretic and model-theoretic notions in one’s logical theory can be shown by soundness and completeness proofs, whether we can define the model-theoretic notions by means of the inferences in a proof system is not at all trivial. For instance, provable inferences in a proof system of classical logic in the logical framework do not determine its intended models as shown by Carnap (Formalization of logic, Harvard University Press, Cambridge, 1943), i.e., there are non-Boolean models (...) that satisfy its provable inferences. In the literature, this is known as the Categoricity problem or Carnap’s problem. In this paper, we will discuss the Categoricity problem (or Carnap’s problem) for three-valued logics K3 and LP. We will provide three different restrictions on admissible models that will deliver us categoricity results, some of which draw from the solutions provided for the Categoricity problem for classical logic in Belnap and Massey (Stud Log 49(1):67–82, 1990) and Bonnay and Westerståhl (Erkenntis 81(4):721–739, 2016). We will then argue that two of those solutions are philosophically well-motivated: (1) restricting the admissible models where negation is interpreted as a Strong Kleene truth-function, and (2) restricting the admissible models where a complex formula is assigned the third value when its immediate subformulas are assigned the third value. (shrink)

In 1973, Rittel and Webber coined the term ‘wicked problems’, which they viewed as pervasive in the context of social and policy planning.1 Wicked problems have 10 defining characteristics: they are not amenable to definitive formulation; it is not obvious when they have been solved; solutions are not true or false, but good or bad; there is no immediate, or ultimate, test of a solution; every implemented solution is consequential, it leaves traces that cannot be undone; there are no criteria (...) to prove that all potential solutions have been identified and considered; every wicked problem is essentially unique; every wicked problem can be considered to be a symptom of another problem; a wicked problem can be explained in numerous ways and the choice of explanation determines what will count as a solution and the actors are liable for the consequences of the actions they generate.1 One needs only a passing familiarity with the history of HIV prevention research, and with the intellectual traditions of research ethics, to appreciate that the perils and opportunities arising from proposals to conduct research with people who inject drugs in some of the most precarious social and political circumstances around the world and the challenges associated with implementing the findings satisfy Rittel's and Webber's criteria for ‘wicked problems’. HIV prevention research has contributed important new knowledge about the feasibility, efficacy or relative efficacy of various prevention strategies in a variety of contexts around the world. But the pathways and timelines for how this knowledge has contributed to improvements in public health practice and/or the establishment of policies that ensure unfettered access to appropriate healthcare services for PWID are less clear and decidedly non-linear. One account of the transition from trial to policy …. (shrink)

The paper discusses problems which arise in attempts to axiomatize parts of religion or religious belief systems. Besides those problems already investigated by Bochenski, like that of the propositional content or the meaning of religious discourse there are several further ones. This paper deals with the question whether full Classical Logic is suitable, whether one universe of discourse is sufficient, how to use definitions and analogous concepts and whether justifications satisfy credibility criteria.

Biological agents can act in ways that express a sensitivity to context-dependent relevance. So far it has proven difficult to engineer this capacity for context-dependent sensitivity to relevance in artificial agents. We give this problem the label the “problem of meaning”. The problem of meaning could be circumvented if artificial intelligence researchers were to design agents based on the assumption of the continuity of life and mind. In this paper, we focus on the proposal made by enactive (...) cognitive scientists to design artificial agents that possess sensorimotor autonomy—stable, self-sustaining patterns of sensorimotor interaction that can ground values, norms and goals necessary for encountering a meaningful environment. More specifically, we consider whether the Free Energy Principle (FEP) can provide formal tools for modeling sensorimotor autonomy. There is currently no consensus on how to understand the relationship between enactive cognitive science and the FEP. However, a number of recent papers have argued that the two frameworks are fundamentally incompatible. Some argue that biological systems exhibit historical path-dependent learning that is absent from systems that minimize free energy. Others have argued that a free energy minimizing system would fail to satisfy a key condition for sensorimotor agency referred to as “interactional asymmetry”. These critics question the claim we defend in this paper that the FEP can be used to formally model autonomy and adaptivity. We will argue it is too soon to conclude that the two frameworks are incompatible. There are undeniable conceptual differences between the two frameworks but in our view each has something important and necessary to offer. The FEP needs enactive cognitive science for the solution it provides to the problem of meaning. Enactive cognitive science needs the FEP to formally model the properties it argues to be constitutive of agency. Our conclusion will be that active inference models based on the FEP provides a way by which scientists can think about how to address the problems of engineering autonomy and adaptivity in artificial agents in formal terms. In the end engaging more closely with this formalism and its further developments will benefit those working within the enactive framework. -/- . (shrink)

The hypothesis that God supernaturally raised Jesus from the dead is argued by William Lane Craig to be the best explanation for the empty tomb and postmortem appearances of Jesus because it satisfies seven criteria of adequacy better than rival naturalistic hypotheses. We identify problems with Craig’s criteria-based approach and show, most significantly, that the Resurrection hypothesis fails to fulfill any but the first of his criteria—especially explanatory scope and plausibility.

Russellian physicalism is a promising answer to the mind–body problem which attempts to satisfy the motivating epistemic and metaphysical concerns of non-physicalists with regards to consciousness, while also maintaining a physicalist commitment to the non-existence of fundamental mentality. Chan (_Philosophical Studies, 178_:2043–62, 2021) has recently described a challenge to Russellian physicalism he deems the ‘difference-maker problem’, which is a Russellian-physicalism-specific version of the more well-known ‘combination problem’ for Russellian monism generally. The problem is to determine how (...) a relatively small set of fundamental categorical property types can ground the large variety of phenomenal properties that exist. To answer this problem, a Russellian physicalist can say that there is strong emergence from fundamental categorical properties to phenomenal properties, or she can say that there is only weak emergence from fundamental categorical properties to phenomenal properties. Chan argues that neither of these routes are viable for Russellian physicalism. This paper constitutes a response to Chan, arguing that Russellian physicalists can embrace either weak or strong emergence to explain phenomenal variety. (shrink)

In this essay I begin with remarks made by Bernard Williams that there are two main motives for philosophy, curiosity and salvation, and that he is not ‘into salvation’. I seek to make the case for the claim that philosophy, at its best, should aim at a kind of ‘salvation’. In the first section, I discuss the problematic character of the world that philosophy should aim to address as a matter of seeking a kind of salvation. I identify this as (...) the problem of ‘cosmodicy’, i.e., the problem of how to justify life in the world as meaningful and worthwhile in the face of extensive evil, suffering, disorder, and the like. In the second section, I discuss how Williams’s claim not to be ‘into salvation’ is not entirely accurate. Although he rejects a certain ‘grand’ traditional picture of salvation, he still seeks a more minimal kind insofar as he addresses the problem of cosmodicy. This comes through in his advocacy of ‘humane’ philosophy and in his attempt to support the values that arise for us from within our historically contingent forms of life. I argue here that Williams is wrong to reject the human concern for a larger cosmic significance. In the final section, I discuss two secular attempts to address the issue of cosmic significance: viz., those of Thomas Nagel and Paolo Costa. I also briefly consider here what a theistic perspective has to offer. I conclude by suggesting that if I am right that philosophy, at is best, should aim at a kind of salvation, then this means that the philosophy of religion should have a central place in any philosophy curriculum. (shrink)

There is evidence that problem-based learning (PBL) is an effective approach to teach team and problem-solving skills, but also to acquire content knowledge. However, there is hardly any literature about using PBL in philosophy classes. One problem is that PBL is resource intensive because a facilitator is needed for each group of students to support learning efforts and monitor group dynamics. In order to establish more PBL classes, the question is whether PBL can be provided without the (...) need for facilitators. We present a combination of five strategies—among them the collaborative argument visualization software AGORA-net—to replace facilitators. Additionally, we present evidence that these strategies are sufficient to provide a PBL experience that achieves intended learning goals in an ethics class and is satisfying for students without facilitators. (shrink)