It is a widely held view in philosophy that propositions perform a plethora of different theoretical roles. Amongst other things, they are believed to be the semantic values of sentences in contexts, the objects of attitudes, the contents of illocutionary acts, and the referents of that-clauses. This assumption is often combined with the claim that propositions have their truth-values eternally. In this paper I aim to show that these two assumptions are incompatible: propositions cannot both fulfill the mentioned roles and (...) be eternally true or false. Following Kaplan and Lewis’s Operator Argument, I argue that compositional semantic values of sentences in contexts do not correspond to eternal propositions. Thus, either we regard the non-eternal entities that in fact realize the semantic role of propositions as also fulfilling the remaining propositional roles, or we abandon the assumption that there is a unique realizer of all the roles. The Operator Argument has recently come under attack, mainly for its tense-logical assumptions. However, rejecting these assumptions is not a sufficient defense of the compatibility of the two claims, since the extensional alternative to the tense-logical framework does not allow us to universally retain eternal propositions as compositional semantic values of sentences either. (shrink)

Feferman, S. and G. Jäger, Systems of explicit mathematics with non-constructive μ-operator. Part I, Annals of Pure and Applied Logic 65 243-263. This paper is mainly concerned with the proof-theoretic analysis of systems of explicit mathematics with a non-constructive minimum operator. We start off from a basic theory BON of operators and numbers and add some principles of set and formula induction on the natural numbers as well as axioms for μ. The principal results then state: BON plus (...) set induction is proof-theoretically equivalent to Peano arithmetic PA; BON plus formula induction is proof-theoretically equivalent to the system <0 of second-order arithmetic. (shrink)

Emerging technologies such as cloud computing, augmented and virtual reality, artificial intelligence and robotics, among others, are transforming the field of manufacturing and industry as a whole in unprecedent ways. This fourth industrial revolution is consequentially changing how operators that have been crucial to industry success go about their practices in industrial environments. This short paper briefly introduces the notion of the Operator 4.0 as well as how this novel way of conceptualizing the human operator necessarily implicates human (...) values in the technologies that constitute it. Similarly, the design methodology known as value sensitive design (VSD) is drawn upon to discuss how these Operator 4.0 technologies can be design for human values and, conversely, how a potential value-sensitive Operator 4.0 can be used to strengthen the VSD methodology in developing novel technologies. (shrink)

The paper is conceived as a first study on the Suszko operator. The purpose of this paper is to indicate the existence of close relations holding between the properties of the Suszko operator and the structural properties of the model class for various sentential logics. The emphasis is put on generality both of the results and methods of tackling the problems that arise in the theory of this operator. The attempt is made here to develop the theory (...) for non-protoalgebraic logics. (shrink)

I argue that ‘actually’ does not have a reading according to which it is synonymous with the actuality operator of modal logic, and propose an alternative account of ‘actually’. The cases that have been thought to show that ‘actually’ is synonymous with the actuality operator are modal and counterfactual sentences in which an embedded clause's evaluation is held fixed at the world of the context. In these cases, though, this embedded clause's evaluation is not due to the presence (...) of ‘actually’. As an alternative, I propose that ‘actually’ is a presupposition trigger along the lines of ‘even’ or ‘too’, and it signals that presupposed information states in the discourse are evolving in a non-standard way. (shrink)

In the debate between relativism and contextualism about various expressions, the Operator Argument, initially proposed by Kaplan , has been taken to support relativism. However, one widespread reaction against the argument has taken the form of arguing against one assumption made by Kaplan: namely, that certain natural language expressions are best treated as sentential operators. Focusing on the only extant version of the Operator Argument proposed in connection to predicates of personal taste such as “tasty” and experiencer phrases (...) such as “for Anna” ), in this paper I investigate whetherthe reasons offered by Cappelen and Hawthorne against various assumptions of the argument failing in the case of modal, temporal, locationaland precisional expressions transfer to the case of experiencer phrases to undercut support for relativism about predicates of personal taste. My aim is to show that they don’t. Thus, I first show that their considerations against experiencer phrases such as “for Anna” being sentential operators are not decisive. Second, I show that even if granting that such experiencer phrases are not sentential operators, a suitably modified version of the Operator Argument can be defended from the objections they raise. (shrink)

This paper is mainly concerned with proof-theoretic analysis of some second-order systems of explicit mathematics with a non-constructive minimum operator. By introducing axioms for variable types we extend our first-order theory BON to the elementary explicit type theory EET and add several forms of induction as well as axioms for μ. The principal results then state: EET plus set induction is proof-theoretically equivalent to Peano arithmetic PA <0).

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.

The power of Wittgenstein's N operator described in the Tractatus is that every proposition which can be expressed in the Russellian variant of the predicate calculus familiar to him has an equivalent proposition in an extended variant of his N operator notation. This remains true if the bound variables are understood in the usual inclusive sense or in Wittgenstein's restrictive exclusive sense. The problematic limit of Wittgenstein's N operator comes from his claim that symbols alone reveal the (...) logical status of propositions. This would require knowledge of the size of the Tractarian domain of unchangeable, simple objects, and this, Wittgenstein maintained, cannot be known. (shrink)

The aim of this article is to give the proof-theoretic analysis of various subsystems of Feferman's theory T1 for explicit mathematics which contain the non-constructive μ-operator and join. We make use of standard proof-theoretic techniques such as cut-elimination of appropriate semiformal systems and asymmetrical interpretations in standard structures for explicit mathematics.

Starting from the formal expressions of the hydrodynamical (or “local”) quantities employed in the applications of Clifford algebras to quantum mechanics, we introduce—in terms of the ordinary tensorial language—a new definition for the field of a generic quantity. By translating from Clifford into tensor algebra, we also propose a new (nonrelativistic) velocity operator for a spin- ${\frac{1}{2}}$ particle. This operator appears as the sum of the ordinary part p/m describing the mean motion (the motion of the center-of-mass), and (...) of a second part associated with the so-called Zitterbewegung, which is the spin “internal” motion observed in the center-of-mass frame (CMF). This spin component of the velocity operator is nonzero not only in the Pauli theoretical framework, i.e., in the presence of external electromagnetic fields with a nonconstant spin function, but also in the Schrödinger case, when the wavefunction is a spin eigenstate. Thus, one gets even in the latter case a decomposition of the velocity field for the Madelung fluid into two distinct parts, which constitutes the nonrelativistic analogue of the Gordon decomposition for the Dirac current. Explicit calculations are presented for the velocity field in the particular cases of the hydrogen atom, of a spherical well potential, and of an electron in a uniform magnetic field. We find, furthermore, that the Zitterbewegung motion involves a velocity field which is solenoidal, and that the local angular velocity is parallel to the spin vector. In the presence of a nonuniform spin vector (Pauli case) we have, besides the component of the local velocity normal to the spin (present even in the Schrödinger theory), also a component which is parallel to the curl of the spin vector. (shrink)

It was shown in [3] (see also [5]) that there is a duality between the category of bounded distributive lattices endowed with a join-homomorphism and the category of Priestley spaces endowed with a Priestley relation. In this paper, bounded distributive lattices endowed with a join-homomorphism, are considered as algebras and we characterize the congruences of these algebras in terms of the mentioned duality and certain closed subsets of Priestley spaces. This enable us to characterize the simple and subdirectly irreducible algebras. (...) In particular, Priestley relations enable us to characterize the congruence lattice of the Q-distributive lattices considered in [4]. Moreover, these results give us an effective method to characterize the simple and subdirectly irreducible monadic De Morgan algebras [7].The duality considered in [4], was obtained in terms of the range of the quantifiers, and such a duality was enough to obtain the simple and subdirectly irreducible algebras, but not to characterize the congruences. (shrink)

In [2] a semantics for implication is offered that makes use of stories — sets of sentences assembled under various constraints. Sentences are evaluated at an actual world and in each member of a set of stories. A sentence B is true in a story s just when B s. A implies B iff for all stories and the actual world, whenever A is true, B is true. In this article the first-order language of [2] is extended by the addition (...) of the operator the story... says that..., as in The story Flashman among the Redskins says that Flashman met Sitting Bull. The resulting language is shown to be sound and complete. (shrink)

Czelakowski introduced the Suszko operator as a basis for the development of a hierarchy of non-protoalgebraic logics, paralleling the well-known abstract algebraic hierarchy of protoalgebraic logics based on the Leibniz operator of Blok and Pigozzi. The scope of the theory of the Leibniz operator was recently extended to cover the case of, the so-called, protoalgebraic π-institutions. In the present work, following the lead of Czelakowski, an attempt is made at lifting parts of the theory of the Suszko (...) operator to the π-institution framework. (shrink)

Fara and Williamson (Mind, 2005) argue that counterpart theory is unable to account for modal claims that use an actuality operator. This paper argues otherwise. Rather than provide a different counterpart translation of the actuality operator itself, the solution presented here starts out with a quantified modal logic in which the actuality operator is redundant, and then translates the sentences of this logic into claims of counterpart theory.

This paper deals with the proof theory of first-order applicative theories with non-constructive μ operator and a form of the bar rule, yielding systems of ordinal strength Γ0 and 20, respectively. Relevant use is made of fixed-point theories with ordinals plus bar rule.

In [14] we used the term finitely algebraizable for algebraizable logics in the sense of Blok and Pigozzi [2] and we introduced possibly infinitely algebraizable, for short, p.i.-algebraizable logics. In the present paper, we characterize the hierarchy of protoalgebraic, equivalential, finitely equivalential, p.i.-algebraizable, and finitely algebraizable logics by properties of the Leibniz operator. A Beth-style definability result yields that finitely equivalential and finitely algebraizable as well as equivalential and p.i.-algebraizable logics can be distinguished by injectivity of the Leibniz (...) class='Hi'>operator. Thus, from a characterization of equivalential logics we obtain a new short proof of the main result of [2] that a finitary logic is finitely algebraizable iff the Leibniz operator is injective and preserves unions of directed systems. It is generalized to nonfinitary logics. We characterize equivalential and, by adding injectivity, p.i.-algebraizable logics. (shrink)

Tarski presented his definition of consequence operator to explain the most important notions which any logical consequence concept must contemplate. A Tarski space is a pair constituted by a nonempty set and a consequence operator. This structure characterizes an almost topological space. This paper presents an algebraic view of the Tarski spaces and introduces a modal propositional logic which has as a model exactly the closed sets of a Tarski space. • DOI:10.5007/1808-1711.2010v14n1p47.

ABSTRACT In this work the connections between the fuzzy closure operators and the graded consequence relations are examined Namely, as it is well known, in the crisp case there is a complete equivalence between the notion of closure operator and the one of consequence relation. We extend this result by proving that the graded consequence relations are related to a particular class of fuzzy closure operators, namely the class of fuzzy closure operators that can be obtained by a chain (...) of classical closure operators. (shrink)

Bergson's views on time are supported by the time operator qualifying complex systems with a concept of time that is essentially difierent from the clock time used to register the events. Irreversibility, unpredictability, and innovation characterize complex systems in contrast with the reversibility, predictability and lack of novelties of the regular motions of integrable systems. The idea for this work came from our teacher Ilya Prigogine who pointed out repeatedly that the time operator actually incorporates Bergson's views on (...) time. We construct a time operator which incorporates Bergson's intuitive views on durations, indeterminism, innovations and irreversibility and the significance of events in terms of inno- vation and aging. In addition, Bergson emphasized that the signif- icance of durations depends on consciousness and memory, a discussion beyond the proposed time operator. Moreover we discuss the relation of Bergson's time with the internal time concepts of Husserl and Heidegger. (shrink)

A system of modal logic with the operator is proposed, and proved complete. In contrast with a previous one by Stalnaker and Thomason, this system does not require two categories of singular terms.

Alarm management is an important task to ensure the safety of industrial process technologies. A well-designed alarm system can reduce the workload of operators parallel with the support of the production, which is in line with the approach of Industry 5.0. Using Process Mining tools to explore the operator-related event scenarios requires a goal-oriented log file format that contains the start and the end of the alarms along with the triggered operator actions. The key contribution of the work (...) is that a method is presented that transforms the historical event data of control systems into goal-oriented log files used as inputs of process mining algorithms. The applicability of the proposed process mining-based method is presented concerning the analysis of a hydrofluoric acid alkylation plant. The detailed application examples illustrate how the extracted process models can be interpreted and utilized. The results confirm that applying the tools of process mining in alarm management requires a goal-oriented log-file design. (shrink)

In this paper we present a tableau system for deontic logics with the operator of explicit permission. By means of this system the decidability of the considered logics can be proved. We will sketch how these logics are semantically defined by means of relating semantics and how they provide a simple solution to the free choice permission problem. In short, these logics employ relating implication and a certain propositional constant. These two are in turn used to define deontic operators (...) similarly as in Andersonian-Kangerian reduction, which uses different intensional implications and constants. (shrink)

The syntax of Frege's scientific language is commonly taken to be characterized by two oddities: the representation of the intended illocutionary role of sentences by a special sign, the judgement-stroke, and the treatment of sentences as a species of singular terms. In this paper, an alternative view is defended. The main theses are: the syntax of Frege's scientific language aims at an explication of the logical form of judgements; the judgement-stroke is, therefore, a truth-operator, not a pragmatic operator; (...) in Frege's first system, '⊦ Δ' expresses that the circumstance Δ is a fact, and in his second system that the truth-value - Δ is the True; in both systems, the judgement-stroke is construed as a sign sui generis, not as a genuine predicate; its counterpart in natural language is the syntactic "form of assertoric sentences", not the truth-predicate; neither in Frege's first nor in his second system sentences are treated as singular terms. (shrink)

To improve the safety and the performance of operators involved in risky and demanding missions, human-machine cooperation should be dynamically adapted, in terms of dialogue or function allocation. To support this reconfigurable cooperation, a crucial point is to assess online the operator’s ability to keep performing the mission. The article explores the concept of Operator Functional State, then it proposes to operationalize this concept on the specific activity of drone swarm monitoring, carried out by 22 participants on simulator (...) SUSIE. With the aid of supervised learning methods, physiological and contextual are classified into three classes, corresponding to different levels of OFS. This classification would help for adapting the countermeasures to the situation faced by operators. (shrink)

Praca jest poświęcona negacji dyskursywnej (metajęzykowej). Omawiane są jej funkcje (np. sprostowanie, uwypuklenie, zaskoczenie), rodzaje (np. implikacyjna, językowa, prozodyczna) i własności (np. pozorna sprzeczność, pragmatyczne odkodowanie, przytoczenie, a nie użycie, brak konstrukcji z prefiksem „nie”, brak konstrukcji z zaimkami negatywnymi). Następnie rozpatrzona została możliwość, że negacja dyskursywna jest jedynie szczególnym przypadkiem innych rodzajów negacji, w szczególności negacji kontrastywnej lub illokucyjnej. Dalej postawiono pytanie, czy w przypadku negacji dyskursywnej mamy do czynienia ze zjawiskiem semantycznym czy pragmatycznym, jak również, czy jest możliwe (...) ujęcie negacji dyskursywnej w ramach mechanizmu konwersacyjnego nazywanego „przywołaniem echem”. (shrink)

In order to develop efficient tools for automated reasoning with inconsistency (theorem provers), eventually making Logics of Formal inconsistency (_LFI_) a more appealing formalism for reasoning under uncertainty, it is important to develop the proof theory of the first-order versions of such _LFI_s. Here, we intend to make a first step in this direction. On the other hand, the logic _Ciore_ was developed to provide new logical systems in the study of inconsistent databases from the point of view of _LFI_s. (...) An interesting fact about _Ciore_ is that it has a _strong_ consistency operator, that is, a consistency operator which (forward/backward) propagates inconsistency. Also, it turns out to be an algebraizable logic (in the sense of Blok and Pigozzi) that can be characterized by means of a 3-valued logical matrix. Recently, a first-order version of _Ciore_, namely _QCiore_, was defined preserving the spirit of _Ciore_, that is, without introducing unexpected relationships between the quantifiers. Besides, some important model-theoretic results were obtained for this logic. In this paper we study some proof–theoretic aspects of both _Ciore_ and _QCiore_ respectively. In first place, we introduce a two-sided sequent system for _Ciore_. Later, we prove that this system enjoys the cut-elimination property and apply it to derive some interesting properties. Later, we extend the above-mentioned system to first-order languages and prove completeness and cut-elimination property using the well-known Shütte’s technique. (shrink)

Modal logics with the binary operator Until are considered. It is shown that there exists a continuum of consistent U-logics without Kripke frames, and that each U-logic whose class of order does not have the finite frame property.

One of the major problems of intrusion detection concerns the large amount of alerts that intrusion detection systems (IDS) produce. Security operator who analyzes alerts and takes decisions, is often submerged by the high number of alerts to analyze. In this paper, we present a new alert correlation approach based on knowledge and preferences of security operators. This approach, which is complementary to existing ones, allows to rank-order produced alerts on the basis of a security operator knowledge about (...) the system, used IDS and his preferences about alerts that he wants to analyze or to ignore. Our approach is based on the development of a new non-classical logic for representing preferences, called FO-MQCL (First Order - Minimal Qualitative Choice Logic). Our logic extends a fragment of the first order logic by adding a new logical connective. The general idea is to present only alerts that fully fit security operator's preferences and knowledge. And if needed, less preferred alerts can also be presented. (shrink)