Automated reasoning issues are addressed for a finite lattice-valued propositional logic LnP(X) with truth-values in a finite lattice-valued logical algebraic structure—lattice implication algebra. We investigate extended strategies and rules from classical logic to LnP(X) to simplify the procedure in the semantic level for testing the satisfiability of formulas in LnP(X) at a certain truth-value level α (α-satisfiability) while keeping the role of truth constant formula played in LnP(X). We propose a lock resolution method at a certain truth-value level α (α-lock (...) resolution) in LnP(X) and have proved its theorems of soundness and weak completeness, respectively. We provide more efficient resolution based automated reasoning in LnP(X) and key supports for α-resolution-based automated reasoning approaches and algorithms in lattice based linguistic truth-valued logic. (shrink)

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)

Satisfiability or Sat\ is the metatheoretic statementEvery formally intuitionistically consistent set of first-order sentences has a model.The models in question are the Tarskian relational structures familiar from standard first-order model theory, but here treated within intuitionistic metamathematics. We prove that both IZF, intuitionistic Zermelo–Fraenkel set theory, and HAS, second-order Heyting arithmetic, prove Sat\ to be false outright. Following the lead of Carter :75–95, 2008), we then generalize this result to some provably intermediate first-order logics, including the Rose logic. These metatheorems (...) distinguish the intuitionistic foundational significance of Sat\ sharply from that of Sat\, the satisfiability claim for intuitionistic propositional logic. At the same time, they establish intuitionistic connections with and between Test, COMP\, and \. Here, Test is the scheme of Testability, and COMP\ and \ are completeness for intuitionistic propositional logic and predicate logic, respectively. (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)

Leibniz said with a mixture of admiration and inspiration that the Duchess Sophie of Hannover always wanted to know the reason why behind the reason why. And that is just how rationality works: it wants to leave no loose ends to understanding, seeking to enable us to understand things through to the bitter end. In the twelve chapters that make up Satisfying Reason, Rescher develops and defends the following perspective: That rationality is a cardinal virtue in cognitive matters. That this (...) is not something simple and cut-and-dried: in the pursuit of truth through the development of knowledge we face obstacles -- sometimes even insuperable ones. All that we can do is the best we can, realizing that even our very best may still be imperfect. Nevertheless, the venture is far from hopeless. While absolutes are unattainable in the cognitive venture, some solutions are situationally optimal, being comparatively the best that can be managed under the circumstances. That reason itself enables us to come to terms with this state of affairs, urging us to accept the best we can do as good enough. Satisfying Reason is an explanation of the presuppositions and methods of rational enquiry, an original exercise in metaknowledge, developing a systematic body of knowledge about the scope and limits of knowledge itself. (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.

The Hilbert–Bernays Theorem establishes that for any satisfiable first-order quantificational schema S, one can write out linguistic expressions that are guaranteed to yield a true sentence of elementary arithmetic when they are substituted for the predicate letters in S. The theorem implies that if L is a consistent, fully interpreted language rich enough to express elementary arithmetic, then a schema S is valid if and only if every sentence of L that can be obtained by substituting predicates of L for (...) predicate letters in S is true. The theorem therefore licenses us to define validity substitutionally in languages rich enough to express arithmetic. The heart of the theorem is an arithmetization of Gödel's completeness proof for first-order predicate logic. Hilbert and Bernays were the first to prove that there is such an arithmetization. Kleene established a strengthened version of it, and Kreisel, Mostowski, and Putnam refined Kleene's result. Despite the later refinements, Kleene's presentation of th.. (shrink)

Setting out to understand the effects of positive moral emotions in leadership, this research examines the consequences of leaders’ expressions of gratitude and pride for their followers. In two experimental vignette studies and a field study, leaders’ gratitude expressions showed a positive effect and leaders’ pride expressions showed a negative effect on followers’ ascriptions of leader selfishness. Thereby, leaders’ gratitude expression indirectly led to higher follower satisfaction with and OCB towards the leader, while leaders’ pride expressions indirectly reduced satisfaction with (...) and OCB towards the leader. Furthermore, leaders’ expressions of gratitude indirectly reduced followers’ intentions to leave the leader, while leaders’ expressions of pride indirectly fuelled them. Although ascriptions of selfishness consistently influenced these leader outcomes more strongly than comparable organizational outcomes, results on organizational outcomes were mixed. While leaders’ expressions of gratitude led, as expected, to higher job satisfaction and lower turnover intentions, leaders’ expressions of pride showed positive relations with both OCB towards the organization and intentions to leave the organization. We discuss the theoretical implications of leaders’ expressions of positive moral emotions as signals of outcome attributions, as well as leaders’ selfishness and practical implications that help leaders build followers’ satisfaction and positive leader–follower relationships. (shrink)

In [4] R.Cowen considers a generalization of the resolution rule for hypergraphs and introduces a notion of satisfiability of families of sets of vertices via 2-colorings piercing elements of such families. He shows, for finite hypergraphs with no one-element edges that if the empty set is a consequence ofA by the resolution rule, thenA is not satisfiable. Alas the converse is true for a restricted class of hypergraphs only, and need not to be true in the general case. In this (...) paper we show that weakening slightly the notion of satisfiability, we get the equivalence of unsatisfiability and the derivability of the empty set for any hypergraph. Moreover, we show the compactness property of hypergraph satisfiability and state its equivalence to BPI, i.e. to the statement that in every Boolean algebra there exists an ultrafilter. (shrink)

Hegel had taken the Kantian categories of thought to be merely formal, without content, since, he argued, Kant abstracted the conditions of thought from the world. The Kantian categories can, as such, only be understood subjectively and so are unable to secure a content for themselves. Hegel, following Fichte, tried to provide a content for the logical categories. In order to reinstate an objective status for logic and conceptuality he tries to affirm the unity of thought and being. The idea (...) that this unity is established by reinstating a pre-Kantian metaphysics has in most of the recent Hegel literature been discredited. In the wake of this non-metaphysical Hegel there is a concern that the architectonic of concepts which is taken as the organizing principle of consciousness offers an account of experience which is too schematic. While Hegel disputes the intuition/concept distinction as it is played out in Kant and Fichte, he does nevertheless retain some residue of a notion of intuition in his theory of the Concept. This is central to understanding his notion of experience as it can't simply be equated with rule governed conceptuality. Satisfying the demands of reason for Hegel requires more than conceiving our experience solely as judgments. (shrink)

Spirituality in the workplace is gaining recognition and value among researchers, academicians, and business professionals. The aim of this paper is to examine the impact of spirituality in the workplace on job satisfaction by measuring four dimensions of spirituality in the workplace: meaningful work, sense of community, organizational values, and compassion. The impact of each dimension on job satisfaction is hypothesized. A cross-sectional survey was used to collect data from 100 payroll employees in private insurance companies in Punjab. A correlation (...) analysis showed a positive relationship between all the dimensions of spirituality in the workplace and job satisfaction. A regression analysis revealed that although all the dimensions of spirituality in the workplace are important, organizational values and a sense of community are the most important in terms of the job satisfaction level of employees. This work will help insurance companies to better understand the concept of spirituality in the workplace and its importance. Insurance companies can improve their functioning by encouraging employee spirituality in the workplace. (shrink)

In this paper, we take up the question of whether there comes a point at which one is no longer morally obliged to do further good, even at very low cost to oneself. More specifically, they ask: under precisely what conditions is it plausible to say that that “point” has been reached? A crude account might focus only on, say, the amount of good the agent has already done, but a moment’s reflection shows that this is indeed too crude. We (...) develop and defend a nuanced account according to which considerations of three types are all relevant to whether one has satisfied one’s duties to assist: “inputs” (types and quantities of sacrifice made), “characteristics” (the beliefs and intentions that informed the donor’s decisions), and “success” (the extent to which the donations in question succeeded in generating value). (shrink)

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.

In ‘The Unsatisfied Paradox’ (The Reasoner 6(12), p.184-5), Peter Eldridge-Smith has argued that no unique solution for the logical paradoxes is likely to exist in the presence of the following two kinds of paradox: 1. The Unsatisfied kind. 2. The Satisfiable kind. We argue that both kinds of paradoxes typically contain some kind of self-reference used for an attempt of self-diagonalization, and that consequently they may solvable in the same way, namely, by the acknowledgement that no intensional object is available (...) to itself for reference or quantification. (shrink)

We investigate how social comparison processes in leader treatment quality impact group members’ self-worth, affect, and behavior. Evidences from the field and the laboratory suggest that employees who are treated kinder and more considerate than their fellow group members experience more self-worth and positive affect. Moreover, the greater positive self-implications of preferentially treated group members motivate them more strongly to comply with norms and to engage in tasks that benefit the group. These findings suggest that leaders face an ethical trade-off (...) between satisfying the moral standard of treating everybody equally well and satisfying individual group members’ desire to be treated better than others. (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)

According to many philosophers, rationality is, at least in part, a matter of one’s attitudes cohering with one another. Theorists who endorse this idea have devoted much attention to formulating various coherence requirements. Surprisingly, they have said very little about what it takes for a set of attitudes to be coherent in general. We articulate and defend a general account on which a set of attitudes is coherent just in case and because it is logically possible for the attitudes to (...) be jointly satisfied in the sense of jointly fitting the world. In addition, we show how the account can help adjudicate debates about how to formulate various rational requirements. (shrink)

In this paper, I explore a fundamental but under-appreciated distinction between two ways of understanding the desire-satisfaction theory of well-being. According to proactive desire satisfactionism, a person is benefited by the acquisition of new satisfied desires. According to reactive desire satisfactionism, a person can be benefited only by the satisfaction of their existing desires. I first offer an overview of this distinction. I then canvass several ways of developing a general formulation of desire satisfactionism that would capture the reactive view, (...) and argue that all come with significant costs. (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)

A compelling requirement on normative theories is that they should be satisfiable, that is, in every possible choice situation with a finite number of alternatives, there should be at least one performable act such that, if one were to perform that act, one would comply with the theory. In this paper, I argue that, given some standard assumptions about free will and counterfactuals, Objective Act Consequentialism violates this requirement.

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)

This paper proposes a new interpretation of John Stuart Mill's notion of utility, which is used to provide a utilitarian justification for an eclectic, rather than a vocational, education. Vocational education is strongly promoted in recent policy documents, which makes it important to raise the question of justification. Many existing interpretations of Mill's utilitarianism argue for a hierarchy of pleasures. Although this enables one to justify an eclectic education, it is an interpretation that could be dismissed as ‘un-utilitarian’. This paper (...) proposes an alternative interpretation of Mill's notion of utility as a hierarchy of preferences. Our interpretation not only provides grounds for justifying an eclectic or critical education, it is also consistent with utilitarianism as an ethical theory. The paper also shows how the resultant curricula will better support democracy and participation in civil society. (shrink)

Within medical ethics, there is widespread agreement that morally valid consent includes an understanding condition. Disagreement centers on what is meant by that understanding condition. Tom Dougherty proposed that this understanding condition should be divided into the two mutually exclusive categories of descriptive information and contextual information. Further, Dougherty argues that each type of information is necessary to satisfy the understanding condition. In contrast, I argue that when the deontic aspect of valid consent is in view, each type of information (...) can be sufficient to satisfy the understanding condition on its own. Moreover, by analyzing delegation, which is conceptually related to consent since both are morally transformative actions, I show that delegation often depends not on descriptive or contextual information but on trust. So, I argue that trustworthiness can also be a type of information that does the same work as descriptive and contextual information in satisfying the understanding condition for valid consent. (shrink)

There is consensus among computer scientists, logicians, and philosophers that good reasoning with qualitative beliefs must have the structural property of cumulative transitivity or, for short, cut. This consensus is typically explicitly argued for partially on the basis of practical and mathematical considerations. But the consensus is also implicit in the approach philosophers take to almost every puzzle about reasoning that involves multiple steps: philosophers typically assume that if each step in reasoning is acceptable considered on its own, the whole (...) chain of reasoning must also acceptable. In this paper I focus on whether there are good philosophical reasons for thinking that the consensus that good reasoning must satisfy cut is true. My central claim is that we should not accept the consensus—good reasoning might not satisfy cut. In particular, I consider four arguments for the consensus and explain why they are unpersuasive. (§2-5). I then show that the issue of whether good reasoning is cut turns on a substantive yet until now unnoticed question in epistemology (§6). (shrink)

We investigate degree of satisfiability questions in the context of Heyting algebras and intuitionistic logic. We classify all equations in one free variable with respect to finite satisfiability gap, and determine which common principles of classical logic in multiple free variables have finite satisfiability gap. In particular we prove that, in a finite non-Boolean Heyting algebra, the probability that a randomly chosen element satisfies $x \vee \neg x = \top $ is no larger than $\frac {2}{3}$. Finally, we generalize our (...) results to infinite Heyting algebras, and present their applications to point-set topology, black-box algebras, and the philosophy of logic. (shrink)

We develop a theoretical model of income and pay comparison satisfaction with two mediators, examine the direct and the indirect paths of our model, and treat culture as a moderator. Based on 311 professors in the US and Spain, we demonstrate a positive direct path and a negative indirect path. Our subsequent multi-group analysis illustrates: For American professors, their direct path shows that income is directly related to high pay comparison satisfaction. Their indirect path reveals the following new insights: Professors (...) with high income have a strong love of money orientation, set their pay equity comparison standards significantly higher than their own salary, and as a consequence, have low pay comparison satisfaction. For Spanish professors, love of money is not related to their pay comparison standards which are slightly higher than their own self-reported income. Neither the direct nor the indirect path is significant. The standardized total effect of income to pay satisfaction is positive for American professors, but negligible for Spanish professors. Are you satisfied with your pay when you compare? Our results demonstrate that pay comparison satisfaction depends on not only one’s income but also one’s love of money and pay equity comparison standards which may vary across cultures. (shrink)

In this paper, I propose a novel theory for why we find certain mundane everyday experiences, objects, and phenomena satisfying aesthetic experiences. I refer to these as 'oddly satisfying' experiences, and argue that they assert themselves as aesthetic by being suggestive of the cinematic. This cinematic quality is the product of everyday experiences gesturing towards a kind of careful artistic intent.

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)

Can opium's tendency to induce sleep be explained by appeal to a "dormitive virtue"? If the label merely references the tendency being explained, the explanation seems vacuous. Yet the presence of a label could signal genuinely explanatory content concerning the (causal) basis for the property being explained. In Experiments 1 and 2, we find that explanations for a person's behavior that appeal to a named tendency or condition are indeed judged to be more satisfying than equivalent explanations that differ only (...) in omitting the name. In Experiment 3, we find support for one proposal concerning what it is about a name that drives a boost in explanatory satisfaction: named categories lead people to draw an inference to the existence of a cause underlying the category, a cause that is responsible for the behavior being explained. Our findings have implications for theories of explanation and point to the central role of causation in explaining behavior. (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)

For any group satisfying a suitable chain condition, we construct a finitely additive measure on it that is invariant under certain actions.

The author addresses the question of the necessity of logic courses in undergraduate education, particularly their use as a requirement in the humanities. This paper outlines why logic counts as a humanities subject and why certain virtues of logic are beneficial to a humanities education. The authors explores these two aspects of the question and invites the reader to decide whether the combination of these two aspects of a logic course jointly satisfy the educational needs of their particular institution’s curriculum.

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)