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.
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.
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 study develops a Science–Technology–Society (STS)-based science ethics education program for high school students majoring in or planning to major in science and engineering. Our education program includes the fields of philosophy, history, sociology and ethics of science and technology, and other STS-related theories. We expected our STS-based science ethics education program to promote students’ epistemological beliefs and moral judgment development. These psychological constructs are needed to properly solve complicated moral and social dilemmas in the fields of science and engineering. (...) We applied this program to a group of Korean high school science students gifted in science and engineering. To measure the effects of this program, we used an essay-based qualitative measurement. The results indicate that there was significant development in both epistemological beliefs and moral judgment. In closing, we briefly discuss the need to develop epistemological beliefs and moral judgment using an STS-based science ethics education program. (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)
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)
The strict-tolerant approach to paradox promises to erect theories of naïve truth and tolerant vagueness on the firm bedrock of classical logic. We assess the extent to which this claim is founded. Building on some results by Girard we show that the usual proof-theoretic formulation of propositional ST in terms of the classical sequent calculus without primitive Cut is incomplete with respect to ST-valid metainferences, and exhibit a complete calculus for the same class of metainferences. We also argue that the (...) latter calculus, far from coinciding with classical logic, is a close kin of Priest’s LP. (shrink)
We define cut-free display calculi for knowledge logics wherean indiscernibility relation is associated to each set of agents, andwhere agents decide the membership of objects using thisindiscernibility relation. To do so, we first translate the knowledgelogics into polymodal logics axiomatised by primitive axioms and thenuse Kracht's results on properly displayable logics to define thedisplay calculi. Apart from these technical results, we argue thatDisplay Logic is a natural framework to define cut-free calculi for manyother logics with relative accessibility relations.
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)
One resolution of the St. Petersburg paradox recognizes that a gamble carries a risk sensitive to the gamble's stakes. If aversion to risk increases sufficiently fast as stakes go up, the St. Petersburg gamble has a finite utility.
Since St. Thomas Aquinas holds that death is a substantial change, a popular current interpretation of his anthropology must be mistaken. According to that interpretation – the ‘survivalist’ view – St. Thomas holds that we human beings survive our deaths, constituted solely by our souls in the interim between death and resurrection. This paper argues that St. Thomas must have held the ‘corruptionist’ view: the view that human beings cease to exist at their deaths. Certain objections to the corruptionist view (...) are also met. (shrink)
In this paper a unified framework for dealing with a broad family of propositional multimodal logics is developed. The key tools for presentation of the logics are the notions of closure relation operation and monotonous relation operation. The two classes of logics: FiRe-logics (finitely reducible logics) and LaFiRe-logics (FiRe-logics with local agreement of accessibility relations) are introduced within the proposed framework. Further classes of logics can be handled indirectly by means of suitable translations. It is shown that the logics from (...) these classes have the finite model property with respect to the class of -formulae, i.e. each -formula has a -model iff it has a finite -model. Roughly speaking, a -formula is logically equivalent to a formula in negative normal form without occurrences of modal operators with necessity force. In the proof we introduce a substantial modification of Claudio Cerrato's filtration technique that has been originally designed for graded modal logics. The main core of the proof consists in building adequate restrictions of models while preserving the semantics of the operators used to build terms indexing the modal operators. (shrink)
In this paper a unified framework for dealing with a broad family of propositional multimodal logics is developed. The key tools for presentation of the logics are the notions of closure relation operation and monotonous relation operation. The two classes of logics: FiRe-logics and LaFiRe-logics are introduced within the proposed framework. Further classes of logics can be handled indirectly by means of suitable translations. It is shown that the logics from these classes have the finite model property with respect to (...) the class of ◇-formulae, i.e. each ◇-formula has a L-model iff it has a finite L-model. Roughly speaking, a ◇-formula is logically equivalent to a formula in negative normal form without occurrences of modal operators with necessity force. In the proof we introduce a substantial modification of Claudio Cerrato's filtration technique that has been originally designed for graded modal logics. The main core of the proof consists in building adequate restrictions of models while preserving the semantics of the operators used to build terms indexing the modal operators. (shrink)
This paper will attempt an investigation of hypothetical intelligent extraterrestrial life from the perspective of the philosophy and theology of St. Thomas Aquinas. Section I will feature an overview of St. Thomas's relevant philosophy of human nature and the differences between human and extraterrestrial natures. Section II will, with special attention to St. Thomas's De malo, treat some possibilities regarding the need for salvation in our hypothetical species. Section III will outline relevant aspects of Thomistic soteriology, especially the reasons behind (...) the Incarnation and the role of human nature in Redemption. Section IV will feature a critique of representatives from the two major schools of scholarly thought on this issue, showing that they either disregard the necessity of a human nature for incorporation into the Mystical Body of Christ or deny the magnitude and singular importance of the Incarnation. Section V will sketch some possibilities for the soteriology of extraterrestrial life using the theology of St. Thomas Aquinas as a framework. (shrink)
Throughout his works, St. Augustine offers at least nine distinct views on the nature of time, at least three of which have remained almost unnoticed in the secondary literature. I first examine each these nine descriptions of time and attempt to diffuse common misinterpretations, especially of the views which seek to identify Augustinian time as consisting of an un-extended point or a distentio animi . Second, I argue that Augustine's primary understanding of time, like that of later medieval scholastics, is (...) that of an accident connected to the changes of created substances. Finally, I show how this interpretation has the benefit of rendering intelligible Augustine's contention that, at the resurrection, motion will still be able to occur, but not time. (shrink)
This paper reviews Deleuze’s theory of language in Logic of Sense, and Deleuze and Guattari’s theory of language in A Thousand Plateaus. In the ontology informed by the Stoics described in those books, human being and language do not exist separately but in a mixture of words and things. The author argues that this flattened ontology of surfaces is incommensurable with the ontology of depth used in conventional humanist qualitative methodology and recommends beginning new empirical inquiry with a concept instead (...) of with method and methodology. (shrink)
Written and set on the banks of the Neva, St Petersburg Dialogues is a startlingly relevant analysis of the human prospect at the end of the twentieth century. As the literary critic George Steiner has remarked, "the age of the Gulag and of Auschwitz, of famine and ubiquitous torture,... nuclear threat, the ecological laying waste of our planet, the leap of endemic, possibly pandemic, illness out of the very matrix of libertarian progress" is exactly what Maistre foretold. In the Dialogues (...) Maistre addressed a number of topics which are discussed briefly or not at all in his other works already available in English. These include an apologetic for traditional Christian beliefs about providence, reflections on the social role of the public executioner and the "divinity" of war, a critique of John Locke's sensationalist psychology, meditations on prayer and sacrifice, and a mini-course on "illuminism." The literary form is that of the "philosophical conversation" -- one that allowed Maistre to be deliberately provocative and to indulge his taste for paradox, a "methodical extravagance" that he judged particularly appropriate for the eighteenth-century salon. Translator and editor Richard Lebrun provides a full scholarly edition of this classic work, complete with an introduction, chronology, critical bibliography, and generous explanatory notes. The Dialogues will be of interest to scholars of literary history as well as the history of ideas. (shrink)
In his epistles, St. Paul sounded a universalism that has recently been taken up by secular philosophers who do not share his belief in Christ, but who regard his project as centrally important for contemporary political life. The Pauline project—as they see it—is the universality of truth, the conviction that what is true is true for everyone, and that the truth should be known by everyone. In this volume, eminent New Testament scholars, historians, and philosophers debate whether Paul's promise can (...) be fulfilled. Is the proper work of reading Paul to reconstruct what he said to his audiences? Is it crucial to retrieve the sense of history from the text? What are the philosophical undercurrents of Paul's message? This scholarly dialogue ushers in a new generation of Pauline studies. (shrink)
It has been argued that St. Thomas Aquinas’s anthropological views fall prey to the problem of “Too Many Thinkers.” The worry, roughly, is that his views entail that I—a human person—am able to think, but that my soul—which is not a human person—is also able to think. Hence, too many thinkers: there are too many ofus having my thoughts. In this paper, I show why this is not a problem for St. Thomas. Along the way, I also address Peter Unger’s (...) argument for substance dualism. (shrink)
The realism grounding St. Thomas Aquinas’s pre-modern natural science defends the reception of similitudes of the forms of things known by abstraction. Modern natural science challenges this abstractio- nist account by recasting «form» in the leading role of principle of intelligibility—instead of forms, modern science discovers laws. Thomistic realism is prima facie incompatible with this account. Following Charles De Koninck, this essay outlines a rapprochement between the epistemology of pre-modern, Thomistic natural science and its modern successor. I argue that natural (...) forms are noetic limits towards which physical laws tend, and our grasp of this tendency uses a mode of knowledge comparable to what St. Thomas termed universal in repraesentando. (shrink)
I reason: (1) For any x, if I knew that A contained x, then the odds are even that B contains either 2x or x/2, so the expected amount in B would be 5x/4. So (2) for all x, if I knew that A contained x, I would have an expected gain in switching to B. So (3) I should switch to B. But this seems clearly wrong, as my information about A and B is symmetrical.
St. Vincent de Paul (1581–1660) is well known for his contribution to charitable and social works. Even though he left no detailed examination of his business practices, by examining his life and his commitment to the poor, it is possible to frame a Vincentian theology of business ethics. Such an understanding would include educating students in the social teaching of the Catholic Church, a preferential option for the poor, good organization, sound business theory, economizing, and a foundation in the liberal (...) arts. (shrink)
