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Reflecting rules: A note on generalizing the deduction theorem

Gillman Payette, G. Payette

Journal of Applied Logic > 2015 > 13 > 3 > 188-196

The purpose of this brief note is to prove a limitative theorem for a generalization of the deduction theorem. I discuss the relationship between the deduction theorem and rules of inference. Often when the deduction theorem is claimed to fail, particularly in the case of normal modal logics, it is the result of a confusion over what the deduction theorem is trying to show. The classic deduction theorem...

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Modeling and verifying probabilistic Multi-Agent Systems using knowledge and social commitments

Khalid Sultan, Jamal Bentahar, Wei Wan, Faisal Al-Saqqar, more

Expert Systems With Applications > 2014 > 41 > 14 > 6291-6304

Multi-Agent Systems (MASs) have long been modeled through knowledge and social commitments independently. In this paper, we present a new method that merges the two concepts to model and verify MASs in the presence of uncertainty. To express knowledge and social commitments simultaneously in uncertain settings, we define a new multi-modal logic called Probabilistic Computation Tree Logic of Knowledge...

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Proof systems for Moss' coalgebraic logic

Marta Bílková, Alessandra Palmigiano, Yde Venema, M. Bilkova, more

Theoretical Computer Science > 2014 > 549 > Complete > 36-60

We study Gentzen-style proof theory of the finitary version of the coalgebraic logic introduced by L. Moss. The logic captures the behaviour of coalgebras for a large class of set functors. The syntax of the logic, defined uniformly with respect to a finitary coalgebraic type functor T, uses a single modal operator ∇T of arity given by the functor T itself, and its semantics is defined in terms of...

article

Krata podwójna: próba opisu wydarzeń przyszłych za pomocą narzędzi logicznych

Albert Przemysław Bażyk

Semina Scientiarum > 2012 > 11

An unflagging interest in describing future events has continuously motivated investigations, particularly in the field of logic.Aristotle, universally acknowledged as the father of logic, proposed a set of certain bases from which we could depart with our investigations. However, these are tools in which, despite their great value, one can perceive certain shortcomings.Over the centuries many attempts...

article

On the Polish “Via Modalization” Approach to Paraconsistency

Ricardo Arturo Nicolás-Francisco

Edukacja Filozoficzna > 2022 > 74 > 161-182

In this paper, I survey the history of the Polish tradition of paraconsistency and its chronological development. I outline the features of this tradition to provide some insights into the more general notion of philosophical schools. The main features of the Polish tradition of paraconsistency are the continuation of research on a previous philosophical tradition and international collaboration.

article

The Uniqueness of Necessary Truth and the Status of S4 and S5

Marco Hausmann

Theoria > 87 > 6 > 1635 - 1650

The aim of this paper is to relate the debate about the status of S4 and S5 as modal logics for metaphysical modality to the debate about the identity of propositions. The necessary truth of the characteristic axioms of S4 and S5 (when interpreted in terms of metaphysical modality) is derived from a view about the identity of propositions, the view that necessarily equivalent propositions are identical.

article

Knowability as De Re Modality: A Certain Solution to Fitch Paradox

Tomasz Jarmużek, Krzysztof Krawczyk, Rafał Palczewski

Roczniki Filozoficzne > 2020 > 68 > 4 > 291-313

Poznawalność jako modalność de re: pewne rozwiązanie paradoksu Fitcha W artykule staramy się znaleźć nowe, intuicyjne rozwiązanie paradoksu Fitcha. Twierdzimy, że tradycyjne wyrażenie zasady poznawalności (p → ◊Kp) opiera się na błędnym rozumieniu poznawalności jako modalności de dicto. Zamiast tego proponujemy rozumieć poznawalność jako modalność de re. W artykule przedstawiamy minimalną logikę poznawalności,...

article

A Sound Interpretation of Leśniewski's Epsilon in Modal Logic KTB

Takao Inoue

Bulletin of the Section of Logic > 2021 > 50 > 4 > 455-463

In this paper, we shall show that the following translation $I^M$ from the propositional fragment $\bf L_1$ of Leśniewski's ontology to modal logic $\bf KTB$ is sound: for any formula $\phi$ and $\psi$ of $\bf L_1$, it is defined as (M1) $I^M(\phi \vee \psi) = I^M(\phi) \vee I^M(\psi)$, (M2) $I^M(\neg \phi) = \neg I^M(\phi)$, (M3) \(I^M(\epsilon ab) = \Diamond p_a \supset p_a . \wedge...

article

Tableau-based translation from first-order logic to modal logic

Tin Perkov, Luka Mikec

Reports on Mathematical Logic > 2021 > Vol. 56 > 57--74

We define a procedure for translating a given first-order formula to an equivalent modal formula, if one exists, by using tableau-based bisimulation invariance test. A previously developed tableau procedure tests bisimulation invariance of a given first-order formula, and therefore tests whether that formula is equivalent to the standard translation of some modal formula. Using a closed tableau as...

article

Rectifying the Mischaracterization of Logic by Mental Model Theorists

Selmer Bringsjord, Naveen Sundar Govindarajulu

Cognitive Science > 44 > 12 > n/a - n/a

Khemlani et al. (2018) mischaracterize logic in the course of seeking to show that mental model theory (MMT) can accommodate a form of inference (

I

, let us label it) they find in a high percentage of their subjects. We reveal their mischaracterization and, in so doing, lay a landscape for future modeling by cognitive scientists who may wonder whether human reasoning is consistent with, or perhaps...

article

New Modification of the Subformula Property for a Modal Logic

Mitio Takano

Bulletin of the Section of Logic > 2020 > 49 > 3 > 255-268

A modified subformula property for the modal logic KD with the additionalaxiom □ ◊(A ∨ B) ⊃ □ ◊ A ∨ □ ◊B is shown. A new modification of the notion of subformula is proposed for this purpose. This modification forms a natural extension of our former one on which modified subformula property for the modal logics K5, K5D and S4.2 has been shown ([2] and [4]). The finite model property as well as decidability...

article

BOULESIC LOGIC, DEONTIC LOGIC AND THE STRUCTURE OF A PERFECTLY RATIONAL WILL

Daniel Rönnedal

Organon F. medzinárodný časopis pre analytickú filozofiu > 2020 > 27 > 2 > 187 – 262

In this paper, I will discuss boulesic and deontic logic and the relationship between these branches of logic. By ‘boulesic logic,’ or ‘the logic of the will,’ I mean a new kind of logic that deals with ‘boulesic’ concepts, expressions, sentences, arguments and systems. I will concentrate on two types of boulesic expression: ‘individual x wants it to be the case that’ and ‘individual x accepts that...

article

Siła i słabość logik modalnych

Marcin Czakon

Filozofia Nauki > 2020 > 28 > 1(109) > 125-132

This is a review of the book Jedność i wielość logik modalnych (The Unity and Diversity of Modal Logics) edited by Marcin Tkaczyk. The book contains discussions of the most recent results of contemporary modal logic, focusing on regular modal logics, epistemic logic, and temporal logic. The book comprises four chapter, each of which deals with selected formal-logical and philosophical problems associated...

article

I.M. Bocheński and Theophrastus’ Modal Logic

Luca Gili

Edukacja Filozoficzna > 2020 > 70 > 23-38

Innocenty Maria Bocheński expounded his interpretation of Theophrastus’ logic chiefly in his book La logique de Théophraste (1947). In Bocheński’s reconstruction, Theophrastus worked on the last insights of Aristotle’s syllogistic and systematized it, thereby opening the door to later (Stoic) developments in the history of logic. A closer look at Bocheński’s interpretation of Theophrastus’ logic can...

article

Semantical Proof of Subformula Property for the Modal Logics K4.3, KD4.3, and S4.3

Daishi Yazaki

Bulletin of the Section of Logic > 2019 > 48 > 4

The main purpose of this paper is to give alternative proofs of syntactical and semantical properties, i.e. the subformula property and the nite model property, of the sequent calculi for the modal logics K4.3, KD4.3, and S4.3. The application of the inference rules is said to be acceptable, if all the formulas in the upper sequents are subformula of the formulas in lower sequent. For some modal logics,...

article

Argumentum Ontologicum and Argumentum Ornithologicum: Anselm of Canterbury and Jorge Luis Borges

J. L. Usó-Doménech, J. A. Nescolarde-Selva, H. Gash

Foundations of Science > 2019 > 24 > 4 > 727-749

In this paper, the authors attempt to prove there is a relationship between Borges’ “Argumentum ornithologicum” and Anselm’s argument “Argumentum ontologicum”. We suggest Borges, using the image of a flock of birds, with oriental reminiscences, half joking, half serious attempts to prove the existence of God. We demonstrate the fallacies incurred by Borges and why his “Argumentum” has no place within...

article

What Are Justification Logics?

Melvin Fitting

Fundamenta Informaticae > 2019 > Vol. 165, nr 3-4 > 193--203

Justification logic began with Sergei Artemov’s work providing an arithmetic semantics for intuitionistic logic. As part of that work, a small number of explicit modal logics were introduced—logics in which there was a structure of terms that kept track of not just what was a necessary truth, but why it was necessary. These explicit modal logics were connected with standard modal logics such as S4,...

article

A Modal Logic of a Truth Definition for Finite Models

Marek Czarnecki, Konrad Zdanowski

Fundamenta Informaticae > 2019 > Vol. 164, nr 4 > 299--325

The property of being true in almost all finite, initial segments of the standard model of arithmetic is ∑⁰₂–complete. Thus, it admits a kind of a truth definition. We define such an arithmetical predicate. Then, we define its modal logic SL and prove a completeness theorem with respect to finite models semantics. The proof that SL is the modal logic of the approximate truth definition for finite...

article

Disappearing Diamonds: Fitch-Like Results in Bimodal Logic

Weng Kin San

Journal of Philosophical Logic > 2019 > 48 > 6 > 1003-1016

Augment the propositional language with two modal operators: □ and ■. Define ♦ $\blacklozenge$ to be the dual of ■, i.e. ♦ ≡ ¬ ■ ¬ $\blacklozenge \equiv \neg \blacksquare \neg$ . Whenever (X) is of the form φ → ψ, let (X ♦ $^{\blacklozenge }$ ) be φ → ♦ ψ $\varphi \rightarrow \blacklozenge \psi$ . (X ♦ $^{\blacklozenge }$ ) can be thought of as the modally qualified...

article

Problem wszechwiedzy logicznej. Krytyka światów nienormalnych i propozycja nowego rozwiązania

Mateusz Klonowski, Krzysztof Krawczyk

Filozofia Nauki > 2019 > 27 > 1(105) > 27-48

In this paper, we bring up the problem of logical omniscience in epistemic logic. One way of avoiding the problem is through Rantala models, where non-normal worlds are introduced. Such models are vulnerable to criticism, as we show. One of many issues that occur is the Bjerring result, which states that incorporating non-normal worlds makes the agent logically incompetent. For this reason, we propose...

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Search results

Reflecting rules: A note on generalizing the deduction theorem

Modeling and verifying probabilistic Multi-Agent Systems using knowledge and social commitments

Proof systems for Moss' coalgebraic logic

Krata podwójna: próba opisu wydarzeń przyszłych za pomocą narzędzi logicznych

On the Polish “Via Modalization” Approach to Paraconsistency

The Uniqueness of Necessary Truth and the Status of S4 and S5

Knowability as De Re Modality: A Certain Solution to Fitch Paradox

A Sound Interpretation of Leśniewski's Epsilon in Modal Logic KTB

Tableau-based translation from first-order logic to modal logic

Rectifying the Mischaracterization of Logic by Mental Model Theorists

New Modification of the Subformula Property for a Modal Logic

BOULESIC LOGIC, DEONTIC LOGIC AND THE STRUCTURE OF A PERFECTLY RATIONAL WILL

Siła i słabość logik modalnych

I.M. Bocheński and Theophrastus’ Modal Logic

Semantical Proof of Subformula Property for the Modal Logics K4.3, KD4.3, and S4.3

Argumentum Ontologicum and Argumentum Ornithologicum: Anselm of Canterbury and Jorge Luis Borges

What Are Justification Logics?

A Modal Logic of a Truth Definition for Finite Models

Disappearing Diamonds: Fitch-Like Results in Bimodal Logic

Problem wszechwiedzy logicznej. Krytyka światów nienormalnych i propozycja nowego rozwiązania

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