Proof Theory of Modal Logic is devoted to a thorough study of proof systems for modal logics, that is, logics of necessity, possibility, knowledge, belief, time, computations etc. It contains many new technical results and presentations of novel proof procedures. The volume is of immense importance for the interdisciplinary fields of logic, knowledge representation, and automated deduction.

The intention of the presented paper is to establish within a certain modal semantic based on the situational ontology a description of the phenomenon of substantial change, which originally had been formulated within Aristotelian metaphysics – a theory based in reistic ontology. We understand substantial changesto be such changes whose subjects are primary substances (πρωται ουσι αι ) conceived as actually existing individual essences. The analysed changeability is of an existential character - it pertains to the existence of those substances. (...) The formalised description of the chosen changes, constructed in part (1) of the study, takes into consideration the necessary condition for their occurrence: the disappearing and coming into being of successively becoming substances. Part (2) presents the manner in which it is possible to reformulate the obtained characteristic of substantial change in order to create a description of a particular variety of situational changes, which belong, in turn, to the intended interpretation of modal sentential logic of change LCG - a calculus in which change is a primitive concept precised with the help of two one-argument operators C and G, read respectively as: it changes that…, a change is enabled by this, that ….. (shrink)

This paper deals with the translation of first order formulas to predicate S5 formulas. This translation does not bring the first order formula itself to a modal system, but modal interpretation of the first order formula can be given by the translation. Every formula can be translated, and the additional condition such as formula's having only one variable, or having both world domain and individual domain is not required. I introduce an indexical predicate 'E' for the translation. The meaning that (...) 'E(a)' is true is 'this world is 'a' '. Because of this meaning, I call 'E' an indexical predicate. 'E' plays an important role for the translation. In addition that the modal formulas can be translated into first order formulas, we can conclude that the first order logic and modal predicate logic isintertranslatable. (shrink)

The Entretiens of the Institut International de Philosophie for 1978 were held in connection with the World Congress of Philosophy in Dusseldorf, from August 27 to September 1. The theme of the Entretiens was Logic and Philosophy. The undersigned, then President of LI.P., was responsible for the planning of the programme. The programme was designed to consist of four sections with the headings Classical and Intuitionist Logic, Modal Logic and its Applications, Inductive Logic and its Applications, (...) and Logic and Epistemology. The aim was also to convey to philosophers who are not experts in logic an informative and representative impression of some of the main sectors of the vast and rapidly expanding field of philosophical logic. At the same time it was thought that this impression should not be conveyed in the form of a series of survey papers but through presentations and discussions of specific topics falling under the main headings men tioned above. For each section a rapporteur was nominated to read a paper and an interlocuteur to comment on it. The programme chairman is grateful that he was able to engage a representative selection of front rank philosophi cal logicians to perform the various tasks. The papers and the comments are printed in this volume in the order in which they appeared in the Programme of the Entretiens. (shrink)

The Third Way is the most interesting and insightful of Aquinas' five arguments for the existence of God, even though it is invalid and has some false premises. With the help of a somewhat weak modal logic, however, the Third Way can be transformed into a argument which is certainly valid and plausibly sound. Much of what Aquinas asserted in the Third Way is possibly true even if it is not actually true. Instead of assuming, for example, that things (...) which are contingent fail to exist at some time, we need only assume that contingent things possibly fail to exist at some time. Likewise, we can replace the assumption that if all things fail to exist at some time then there is a time when nothing exists, with the corresponding assumption that if all things possibly fail to exist at some time then possibly there is a time when nothing exists. These and other similar replacements suffice to produce a cogent cosmological argument. (shrink)

Anti-realists about the past claim that no one has yet manifested a knowledge of the truth of tensed instances of the realist schema '‡,' instances such as '‡. It is true that we cannot decide specific instances of the realist schema and that, consequently, neither our understanding of these instances, nor our knowledge of their truth may be constituted by the recognitional and executive capacities which, according to Michael Dummett's antirealism, constitute grasp of meaning. Although we cannot decide these issues, (...) we can meet Dummett's anti-realist's manifestability challenge by arguing for them from contingency. While no recognitional and decisional skills may constitute our knowledge that their truth-conditions are satisfied, we can, without begging the question, derive that knowledge from our folk and scientific theories of the workings of nature. The evidence we have in favor of the fact that evidential relations between us and past facts are naturally contingent allows us to infer tensed instances of the fundamental realist modal claim. The joint possibility of truth and undecideability pro tempora is a natural possibility and, thereby, a logical and metaphysical possibility. (shrink)

The problem I tackle in this article is: Do we have in Scotus a modal logic or a counterpart theory? We need to take a rather roundabout path to handle this problem. This is because, whether it be in Lewis's original formulation or in others' applications, the crucial concept of 'counterpart' has never been clearly explicated. In section two, I shall therefore examine the recent controversy concerning Leibniz's views on modalities which centers around the counterpart relation. By fully exploiting (...) the lessons learned from such an examination, I shall then launch a trilemma against a Leibnizian in section three. Section four shall make the claim that unlike Leibniz's case, Scotus's position is not endangered by the trilemma. One important premise will be adopted from my thesis presented elsewhere regarding the different between Scotus's haecceitas and Leibniz's individual essence. Another will be secured from a brief report on Scotus's views on similarity, which might be utterly original to modern eyes jaundiced by contemporary set theories. (shrink)

Provability, Computability and Reflection.

In “Elementa Juris Naturalis” (1671) G.W. Leibniz formulated the genius intuition about the fundamental unity of juridical and Aristotelian modalities. Interpreting and explicating this intuition by virtue of the deontic logic G.W. Wright arrived to the conclusion that the unity of modalities in question is not an equivalence relation but an analogy one. However a complement for G.W. Wright’s explication of the intuition of G.W. Leibniz was submitted. This complement was a two-valued algebra of formal-natural-law philosophy of juridical and (...) Aristotelian modalities as moral-legal evaluation-functions determined by one variable. In thepresent paper I submit a binary generalization of the mentioned unary complement. By virtue of this generalization some significant shortcomings of the complement in question are eliminated. The generalization deals with the modalities as moral-legal evaluation-functions determined by two variables. (shrink)

If the notion of speech acts is to be taken seriously, it must be possible to treat speech acts as acts. The development of systems of DEL (dynamic epistemic logic) in the last two decades suggests an interesting possibility. These systems are developed on the basis of static epistemic logics by introducing model updating operations to interpret various kinds of speech acts including public announcements as well as private information transmissions as what update epistemic states of agents involved. The (...) methods used in developing DEL can be used to develop logics that deal with a much wider variety of speech acts. For example, in ECL (Eliminative Command Logic) of Yamada (2007a) and ECL II of Yamada (2007b), similar model updating operations are introduced tointerpret acts of commanding as what update deontic aspects of the situations in which agents are involved. In Yamada (2008a), ECL II is further extended so as to model acts of promising along with acts of commanding. Moreover, in Yamada (2008b), ECL II is combined with a modified version of DEUL (dynamic epistemic upgrade logic) introduced in van Benthem & Liu (2007). In the resulting logic DDPL (dynamic deontic preference logic), illocutionary acts of commanding are differentiated from preference upgrading perlocutionary acts. The development of these logics suggests a recipe for developing logics that deal with various specific speech acts: first, carefully identify the aspects affected by the speech acts you want to study; second, find the modal logic that characterizes the aspects in question; and finally, add dynamic modalities that stand for the types of the speech acts being studied and define model updating operation that interprets these speech acts as what update the very aspects. (shrink)

The document titled “14 points of Wilson” was announced by the President of the United States Woodrow Wilson in his speech addressed to the United States Congress on 8th January 1918. The speech is one of the most well known documents of the First World War as it touched upon several world issues. The text has been interpreted ever since in respect to the importance and real meaning of points formulated by Wilson. One of the points referred to Poland. The (...) aim of the paper is to focus on the exponents of deontic modality used in that text of historical value and to find the answer to the question concerning the deontic value of each point. The analysis will encompass the principles of deontic logic as well as the meaning of deontic modals in legal discourse at the time of speech delivery as those 14 points should be classified as a text belonging to legal genres. The aim of the paper is to present the historical background and the linguistic analysis in order to find out whether historical facts, interpretations and language used correspond with one another. (shrink)

Presented here are translations of two essays of the Austrian logician, philosopher and experimental psychologist Ernst Mally, originally delivered at the Third International Congress of Philosophy in Heidelberg, Germany. Both essays conclude with discussion between Mally and Kurt Grelling. Mally was a student of Alexius Meinong and a contributor to logical investigations in the field of object theory (Gegenstandstheorie). In these essays, Mally introduces a vital distinction between formal and extra-formal ?determinations? (Bestimmungen), and he argues that formal determinations are not (...) part of the identity conditions for intended objects, but provide the basis for a theory of pure logical and mathematical relations. Mally then proceeds to develop a formal logic of formal and extra-formal determinations, whose interrelations of ontic and modal predications provide an analysis of fundamental object theory concepts. (shrink)

After explaining the interdisciplinary aspect of the series of events organized around the square of opposition since 2007, we discuss papers related to the 4th World Congress on the Square of Opposition which was organized in the Vatican at the Pontifical Lateran University in 2014. We distinguish three categories of work: those dealing with the evolution and development of the theory of opposition, those using the square as a metalogical tool to give a better understanding of various systems of (...) class='Hi'>logic and those related with applications of the theory of opposition to conceptual analysis and pedagogy. (shrink)

Some options to single out the foremost function of philosophy in culture are discussed. As any functioning part has to possess definite level of the internal unity, I begin by tracing out the main views on the unanimity of philosophical knowledge and demonstrate that the opposed variants can be reduced to well‐known contraposition between subject matter (a strong variant) and method (a weak one). I show further that at least one strong version, which identifies philosophical subject matter with the concrete (...) universal being, seizes on only one piece of metaphysics. As a result, the boundary line between strong and weak versions erodes and the strong version converges into the weak one. Finally, I argue that fundamental philosophical themes can be united on the base of three famous Kant’s questions: What can I know? What may I hope? What ought I to do? Difference across modalities testifies against the interpretation of these questions as synopsis. Moreover, these questions correlate well with the three core parts of the making‐decision situation. Such a situation includes a set of possible alternatives and a system or an aggregate of selection criteria for a choice of the variant desired. These two components are logically prior to goal setting. Clearly, to achieve desired object one is to determine what steps are necessary for success. It is no less clear that in the structure of an action, they represent something one ought to do. Thus, specific cultural mission of philosophizing lies in the design and justification of Weltanschauung. (shrink)