Online research in philosophy

This book gives a comprehensive overview of central themes of finite model theory – expressive power, descriptive complexity, and zero-one laws – together with selected applications relating to database theory and artificial intelligence, especially constraint databases and constraint satisfaction problems. The final chapter provides a concise modern introduction to modal logic, emphasizing the continuity in spirit and technique with finite model theory. This underlying spirit involves the use of various fragments of and hierarchies within first-order, second-order, fixed-point, and infinitary logics (...) to gain insight into phenomena in complexity theory and combinatorics. The book emphasizes the use of combinatorial games, such as extensions and refinements of the Ehrenfeucht-Fraissé pebble game, as a powerful way to analyze the expressive power of such logics, and illustrates how deep notions from model theory and combinatorics, such as o-minimality and treewidth, arise naturally in the application of finite model theory to database theory and AI. Students of logic and computer science will find here the tools necessary to embark on research into finite model theory, and all readers will experience the excitement of a vibrant area of the application of logic to computer science. (shrink)

Contrary to the common view, this paper suggests that the Hippocratic oath does not directly refer to the controversial subjects of euthanasia and abortion. We interpret the oath in the context of establishing trust in medicine through departure from Pantagruelism. Pantagruelism is coined after Rabelais' classic novel Gargantua and Pantagruel. His satire about a wonder herb, Pantagruelion, is actually a sophisticated model of anti-medicine in which absence of independent moral values and of properly conducted research fashion a flagrant over-medicalization of (...) human problems. Ultimately this undermines the therapeutic core of medicine itself. We contend that PAS is a case of such over-medicalization and that its institution creates medicophobia. This article does not express an opinion about euthanasia in general. Rather, we claim that physicians should learn from the oath and from Rabelais that they should keep their practice to medical care and not to exploit their expertise and social privileges for the sake of ulterior motives, even when their patients desire those goals. (shrink)

The article calls for a departure from the common concept of autonomy in two significant ways: it argues for the supremacy of semantic understanding over procedure, and claims that clinicians are morally obliged to make a strong effort to persuade patients to accept medical advice. We interpret the value of autonomy as derived from the right persons have to respect, as agents who can argue, persuade and be persuaded in matters of utmost personal significance such as decisions about medical care. (...) Hence, autonomy should and could be respected only after such an attempt has been made. Understanding suffering to a significant degree is a prerequisite to sincere efforts of persuasion. It is claimed that a modified and pragmatic form of discourse is the necessary framework for understanding suffering and for compassionately interacting with the frail. (shrink)

What is an inference rule? This question does not have a unique answer. One usually finds two distinct standard answers in the literature; validity inference $(\sigma \vdash_\mathrm{v} \varphi$ if for every substitution τ, the validity of τ [σ] entails the validity of τ[φ]), and truth inference $(\sigma \vdash_\mathrm{t} \varphi$ if for every substitution τ, the truth of τ[σ] entails the truth of τ[φ]). In this paper we introduce a general semantic framework that allows us to investigate the notion of inference (...) more carefully. Validity inference and truth inference are in some sense the extremal points in our framework. We investigate the relationship between various types of inference in our general framework, and consider the complexity of deciding if an inference rule is sound, in the context of a number of logics of interest: classical propositional logic, a nonstandard propositional logic, various propositional modal logics, and first-order logic. (shrink)

This article isolates ten prepositions, which constitute the undercurrent paradigm of contemporary discourse of health disease and medicine. Discussion of the interrelationship between those prepositions leads to a systematic refutation of this paradigm. An alternative set is being forwarded. The key notions of the existing paradigm are that health is the natural condition of humankind and that disease is a deviance from that nature. Natural things are harmonious and healthy while human made artifacts are coercive interference with natural balance. It (...) is suggested that the current paradigm is influenced by the world of finances and by instrumental reason. The alternative model suggests that human nature cannot be delineated. Humans fashion their own selves and nature by artificial means, medicine among them. The article discusses the implications of the paradigm adapted in various scholarly and popular debates such as the use of sex hormones for contraception, the care of the elderly, holistic medicine and distributive justice in health care. Medicine is not an isolated or a privileged realm. There is no unique entitlement to health care. It is always part of a broader agenda of social values and institutions. A open view of human societies, values and practices as they are situated within concrete material conditions is the platform required for an integrative and creative discourse of health care. (shrink)

In program synthesis, we transform a specification into a system that is guaranteed to satisfy the specification. When the system is open, then at each moment it reads input signals and writes output signals, which depend on the input signals and the history of the computation so far. The specification considers all possible input sequences. Thus, if the specification is linear, it should hold in every computation generated by the interaction, and if the specification is branching, it should hold in (...) the tree that embodies all possible input sequences. Often, the system cannot read all the input signals generated by its environment. For example, in a distributed setting, it might be that each process can read input signals of only part of the underlying processes. Then, we should transform a specification into a system whose output depends only on the readable parts of the input signals and the history of the computation. This is called synthesis with incomplete information. In this work we solve the problem of synthesis with incomplete information in its full generality. We consider linear and branching settings with complete and incomplete information. We claim that alternation is a suitable and helpful mechanism for coping with incomplete information. Using alternating tree automata, we show that incomplete information does not make the synthesis problem more complex, in both the linear and the branching paradigm. In particular, we prove that independently of the presence of incomplete information, the synthesis problems for CTL and CTL * are complete for EXPTIME and 2EXPTIME, respectively. (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)

If K is an index of relative voting power for simple voting games, the bicameral postulate requires that the distribution of K -power within a voting assembly, as measured by the ratios of the powers of the voters, be independent of whether the assembly is viewed as a separate legislature or as one chamber of a bicameral system, provided that there are no voters common to both chambers. We argue that a reasonable index – if it is to be used (...) as a tool for analysing abstract, ‘uninhabited’ decision rules – should satisfy this postulate. We show that, among known indices, only the Banzhaf measure does so. Moreover, the Shapley–Shubik, Deegan–Packel and Johnston indices sometimes witness a reversal under these circumstances, with voter x ‘less powerful’ than y when measured in the simple voting game G1 , but ‘more powerful’ than y when G1 is ‘bicamerally joined’ with a second chamber G2 . Thus these three indices violate a weaker, and correspondingly more compelling, form of the bicameral postulate. It is also shown that these indices are not always co-monotonic with the Banzhaf index and that as a result they infringe another intuitively plausible condition – the price monotonicity condition. We discuss implications of these findings, in light of recent work showing that only the Shapley–Shubik index, among known measures, satisfies another compelling principle known as the bloc postulate. We also propose a distinction between two separate aspects of voting power: power as share in a fixed purse (P-power) and power as influence (I-power). (shrink)