Over the past 15 years, a great deal of efforts have been done by political philosophers to make liberal political theory more sensitive to the importance culture has for individuals, and to think about how to translate this importance into laws and policies, in particular those affecting cultural and national minorities. However, one of the outstanding issues is whether and how an appropriate account of the worth of culture can be provided from a liberal point of view. The most important (...) and currently discussed liberal defence of the worth of culture is probably expressed in Will Kymlicka's theory of minority rights. Such a defence argues for the instrumental role culture plays in people's ability to make meaningful choices and lead a self-directed existence. This paper seeks to show that Kymlicka's instrumental account of the worth of cultures is non-viable, and that a liberal conception of culture viewed as intrinsically valuable is indispensable. While each of them recognizes individual autonomy as an intrinsically valuable good, it is demonstrated that both differ not only as to the role culture has to play in a self-directed existence, but also as to why cultures deserve to be protected and as to their policies towards non-liberal minority cultures. (shrink)

This volume offers an English translation of John of St. Thomas's Cursus theologicus I, question I, disputation 2. In this particular text, the Dominican master raises questions concerning the scientific status and nature of theology. At issue, here, are a number of factors: namely, Christianity's continual coming to terms with the "Third Entry" of Aristotelian thought into Western Christian intellectual culture - specifically the Aristotelian notion of 'science' and sacra doctrina's satisfaction of those requirements - the Thomistic-commentary tradition, and the (...) larger backdrop of the Iberian Peninsula's flourishing "Second Scholasticism." In this latter context, John of St. Thomas applies the theological principles of Thomas Aquinas to the Scholastic disputes preoccupying Thomist, Franciscan, and Jesuit theologians, such as Cajetan, Bañez, Luis de Molina, Vazquez, Suárez - to name only a few - in a tour de force of theological thinking throughout the entire period of Scholasticism. In the process - and not insignificantly - the status quaestionis of theology's scientific character is clearly framed and answered according to John's satisfaction. Key to John of St. Thomas's resolution of the question is his understanding of the continuity of the power of human reason with the super-intelligibility of divine revelation spelled out in terms of what he calls "virtual revelation." This text presented in this volume is a quintessential example of the deep and abiding harmony that flourished between faith and reason as well as grace and nature within the golden era of Baroque Scholasticism. (shrink)

This is a very good book. It gives 205 inscriptions from ten of the Cycladic islands. A number of them are published here for the first time. In their majority they are either funerary or invocations for divine help. Some are dedicatory. Some are inscriptions on well-paintings identifying the scene or the saint depicted or being themselves dedicatory or invocatory. Some are in praise of God or in thanks to God. Some are exhortations to the faithful or quotations from the (...) Scriptures. Two are boundary stones and two are magical exorcisms. Outstanding among them are the cadastre of the area of Perissa on the island of Thera, the invocations for divine help carved by weatherbeaten seafarers on the rocks of the desert cove of Grammata on the island of Syros, and the intriguing 60-odd funerary inscriptions of the angels, also from Thera, that keep defying explanation. As a whole they give an insight and lead to a close intimacy with the life of the islanders in these early centuries, fortified as they were by the christian faith, toiling on the thin soil of their land and venturing at sea. Some of them raise questions that cannot be easily answered. Others are quite straightforward. (shrink)

In the World Library of Psychologists series, international experts themselves present career-long collections of what they judge to be their finest pieces - extracts from books, key articles, salient research findings, and their major theoretical and practical contributions. Jonathan St B T Evans is amongst the foremost cognitive psychologists of his generation, having been influential in spearheading developments in the psychological study of reasoning from its very beginnings in the 1970s up to the present day. This volume of self-selected papers (...) recognises Professor Evan's major contribution to the psychological study of thinking and reasoning by bringing together his most influential and important works. Early selections in the book focus upon experimental studies of reasoning - matching bias in the Wason selection task, belief bias in syllogistic reasoning, and also seminal work on the understanding of conditional statements. The later selections include Evans' work on more general forms of dual process and dual system theory, and his recent account of two minds in one brain. The volume also contains chapters which highlight Evans' contribution to the topic of human rationality, and also his influence on the development of the "new paradigm" in the psychology of reasoning. The key developments in the psychology of reasoning are paralleled by those in Evans's own intellectual history, and the book will therefore make essential reading for all researchers in the psychology of reasoning, and a wider audience of graduate and upper-level undergraduate students with an interest in reasoning and/or dual process theory. (shrink)

We show the completeness of a Hilbert-style system LK defined by M. Valiev involving the knowledge operator K dedicated to the reasoning with incomplete information. The completeness proof uses a variant of Makinson's canonical model construction. Furthermore we prove that the theoremhood problem for LK is co-NP-complete, using techniques similar to those used to prove that the satisfiability problem for propositional S5 is NP-complete.

We provide a simple translation of the satisfiability problem for regular grammar logics with converse into GF2, which is the intersection of the guarded fragment and the 2-variable fragment of first-order logic. The translation is theoretically interesting because it translates modal logics with certain frame conditions into first-order logic, without explicitly expressing the frame conditions. It is practically relevant because it makes it possible to use a decision procedure for the guarded fragment in order to decide regular grammar logics with (...) converse. The class of regular grammar logics includes numerous logics from various application domains. A consequence of the translation is that the general satisfiability problem for every regular grammar logics with converse is in EXPTIME. This extends a previous result of the first author for grammar logics without converse. Other logics that can be translated into GF2 include nominal tense logics and intuitionistic logic. In our view, the results in this paper show that the natural first-order fragment corresponding to regular grammar logics is simply GF2 without extra machinery such as fixed-point operators. (shrink)

We provide a simple translation of the satisfiability problem for regular grammar logics with converse into GF2, which is the intersection of the guarded fragment and the 2-variable fragment of first-order logic. The translation is theoretically interesting because it translates modal logics with certain frame conditions into first-order logic, without explicitly expressing the frame conditions. It is practically relevant because it makes it possible to use a decision procedure for the guarded fragment in order to decide regular grammar logics with (...) converse. The class of regular grammar logics includes numerous logics from various application domains. A consequence of the translation is that the general satisfiability problem for every regular grammar logics with converse is in EXPTIME. This extends a previous result of the first author for grammar logics without converse. Other logics that can be translated into GF2 include nominal tense logics and intuitionistic logic. In our view, the results in this paper show that the natural first-order fragment corresponding to regular grammar logics is simply GF2 without extra machinery such as fixed-point operators. (shrink)

We study a knowledge logic that assumes that to each set of agents, an indiscernibility relation is associated and the agents decide the membership of objects or states up to this indiscernibility relation. Its language contains a family of relative knowledge operators. We prove the decidability of the satisfiability problem, we show its EXPTIME-completeness and as a side-effect, we define a complete Hilbert-style axiomatization.

This paper concerns model-checking of fragments and extensions of CTL* on infinite-state Presburger counter systems, where the states are vectors of integers and the transitions are determined by means of relations definable within Presburger arithmetic. In general, reachability properties of counter systems are undecidable, but we have identified a natural class of admissible counter systems (ACS) for which we show that the quantification over paths in CTL* can be simulated by quantification over tuples of natural numbers, eventually allowing translation of (...) the whole Presburger-CTL* into Presburger arithmetic, thereby enabling effective model checking. We provide evidence that our results are close to optimal with respect to the class of counter systems described above. (shrink)

Like modal logic, temporal logic, and description logic, separation logic has become a popular class of logical formalisms in computer science, conceived as assertion languages for Hoare-style proof systems with the goal to perform automatic program analysis. In a broad sense, separation logic is often understood as a programming language, an assertion language and a family of rules involving Hoare triples. In this survey, we present similarities between separation logic as an assertion language and modal and temporal logics. Moreover, we (...) propose a selection of landmark results about decidability, complexity and expressive power. (shrink)

Motivated by the verification of programs with pointer variables, we introduce a temporal logic whose underlying assertion language is the quantifier-free fragment of separation logic and the temporal logic on the top of it is the standard linear-time temporal logic LTL. We analyze the complexity of various model-checking and satisfiability problems for , considering various fragments of separation logic , various classes of models , and the influence of fixing the initial memory state. We provide a complete picture based on (...) these criteria. Our main decidability result is pspace-completeness of the satisfiability problems on the record fragment and on a classical fragment allowing pointer arithmetic. -completeness or -completeness results are established for various problems by reducing standard problems for Minsky machines, and underline the tightness of our decidability results. (shrink)

This work is divided in two papers (Part I and Part II). In Part I, we study a class of polymodal logics (herein called the class of "Rare-logics") for which the set of terms indexing the modal operators are hierarchized in two levels: the set of Boolean terms and the set of terms built upon the set of Boolean terms. By investigating different algebraic properties satisfied by the models of the Rare-logics, reductions for decidability are established by faithfully translating the (...) Rare-logics into more standard modal logics. The main idea of the translation consists in eliminating the Boolean terms by taking advantage of the components construction and in using various properties of the classes of semilattices involved in the semantics. The novelty of our approach allows us to prove new decidability results (presented in Part II), in particular for information logics derived from rough set theory and we open new perspectives to define proof systems for such logics (presented also in Part II). (shrink)

We present an overview of linear-time temporal logics with Presburger constraints whose models are sequences of tuples of integers. Such formal specification languages are well-designed to specify and verify systems that can be modelled with counter systems. The paper recalls the general framework of LTL over concrete domains and presents the main decidability and complexity results related to fragments of Presburger LTL. Related formalisms are also briefly presented.

La pensée et la sagesse sont universelles, traversent les lieux et les temps, en unissant les hommes. Bouddhistes et philosophes examinent ici " la merveilleuse concordance " que Schopenhauer, à l'aube du monde contemporain, relevait entre sa philosophie et la sagesse millénaire du Bouddha. Les textes présentés ici sont les versions intégrales des conférences prononcées lors du colloque " Sakyamuni et Schopenhauer " qui s'est tenu au Dharma Ling de Paris les 13 et 14 mars 2004 sous l'égide de L'UDHAO.

This work is divided in two papers (Part I and Part II). In Part I, we introduced the class of Rare-logics for which the set of terms indexing the modal operators are hierarchized in two levels: the set of Boolean terms and the set of terms built upon the set of Boolean terms. By investigating different algebraic properties satisfied by the models of the Rare-logics, reductions for decidability were established by faithfully translating the Rare-logics into more standard modal logics (some (...) of them contain the universal modal operator).In Part II, we push forward the results from Part I. For Rare-logics with nominals (present at the level of formulae and at the level of modal expressions), we show that the constructions from Part I can be extended although it is technically more involved. We also characterize a class of standard modal logics for which the universal modal operator can be eliminated as far as satifiability is concerned. Although the previous results have a semantic flavour, we are also able to define proof systems for Rare-logics from existing proof systems for the corresponding standard modal logics. Last, but not least, decidability results for Rare-logics are established uniformly, in particular for information logics derived from rough set theory. (shrink)

There exist valuable methods for theorem proving in non classical logics based on translation from these logics into first-order classical logic (abbreviated henceforth FOL). The key notion in these approaches istranslation from aSource Logic (henceforth abbreviated SL) to aTarget Logic (henceforth abbreviated TL). These methods are concerned with the problem offinding a proof in TL by translating a formula in SL, but they do not address the very important problem ofpresenting proofs in SL via a backward translation. We propose a (...) framework for presenting proofs in SL based on a partial backward translation of proofs obtained in a familiar TL: Order-Sorted Predicate Logic. The proposed backward translation transfers some formulasF TL belonging to the proof in TL into formulasF SL , such that the formulasF SL either (a) belong to a corresponding deduction in SL (in the best case) or, (b) are semantically related in some precise way, to formulas in the corresponding deduction in SL (in the worst case). The formulasF TL andF SL can obviously be considered aslemmas of their respective proofs. Therefore the transfer of lemmas of TL gives at least a skeleton of the corresponding proof in SL. Since the formulas of a proof keep trace of the strategy used to obtain the proof, clearly the framework can also help in solving another fundamental and difficult problem:the transfer of strategies from classical to non classical logics. We show how to apply the proposed framework, at least to S5, S4(p), K, T, K4. Two conjectures are stated and we propose sufficient (and in general satisfactory) conditions in order to obtain formulas in the proof in SL. Two particular cases of the conjectures are proved to be theorems. Three examples are treated in full detail. The main lines of future research are given. (shrink)