Proof Systems for a Gödel Modal Logic

2009 ◽  
pp. 265-279 ◽  
Author(s):  
George Metcalfe ◽  
Nicola Olivetti
Keyword(s):  
Modal Logic ◽  
Proof Systems

PROOF SYSTEMS FOR VARIOUS FDE-BASED MODAL LOGICS

2019 ◽  
Vol 13 (4) ◽  
pp. 720-747
Author(s):  
SERGEY DROBYSHEVICH ◽  
HEINRICH WANSING
Keyword(s):  
Modal Logic ◽  
Sequent Calculus ◽  
Axiom System ◽  
Modal Logics ◽  
Cut Elimination ◽  
Proof Systems ◽  
Image Position ◽  
Axiomatic Extension

AbstractWe present novel proof systems for various FDE-based modal logics. Among the systems considered are a number of Belnapian modal logics introduced in Odintsov & Wansing (2010) and Odintsov & Wansing (2017), as well as the modal logic KN4 with strong implication introduced in Goble (2006). In particular, we provide a Hilbert-style axiom system for the logic $BK^{\square - } $ and characterize the logic BK as an axiomatic extension of the system $BK^{FS} $. For KN4 we provide both an FDE-style axiom system and a decidable sequent calculus for which a contraction elimination and a cut elimination result are shown.

scholarly journals WHAT IS THE CORRECT LOGIC OF NECESSITY, ACTUALITY AND APRIORITY?

2014 ◽  
Vol 7 (3) ◽  
pp. 385-414 ◽  
Author(s):  
PETER FRITZ
Keyword(s):  
Normal Form ◽  
Modal Logic ◽  
Two Dimensional ◽  
Propositional Modal Logic ◽  
Relational Structures ◽  
Proof Systems ◽  
Form Theorem ◽  
Actuality Operator ◽  
Normal Form Theorem ◽  
Soundness And Completeness

AbstractThis paper is concerned with a propositional modal logic with operators for necessity, actuality and apriority. The logic is characterized by a class of relational structures defined according to ideas of epistemic two-dimensional semantics, and can therefore be seen as formalizing the relations between necessity, actuality and apriority according to epistemic two-dimensional semantics. We can ask whether this logic is correct, in the sense that its theorems are all and only the informally valid formulas. This paper gives outlines of two arguments that jointly show that this is the case. The first is intended to show that the logic is informally sound, in the sense that all of its theorems are informally valid. The second is intended to show that it is informally complete, in the sense that all informal validities are among its theorems. In order to give these arguments, a number of independently interesting results concerning the logic are proven. In particular, the soundness and completeness of two proof systems with respect to the semantics is proven (Theorems 2.11 and 2.15), as well as a normal form theorem (Theorem 3.2), an elimination theorem for the actuality operator (Corollary 3.6), and the decidability of the logic (Corollary 3.7). It turns out that the logic invalidates a plausible principle concerning the interaction of apriority and necessity; consequently, a variant semantics is briefly explored on which this principle is valid. The paper concludes by assessing the implications of these results for epistemic two-dimensional semantics.

scholarly journals A Tableau Proof System with Names for Modal Mu-calculus

10.29007/lwqm ◽  
2018 ◽  
Author(s):  
Colin Stirling
Keyword(s):  
Modal Logic ◽  
Expressive Power ◽  
Proof System ◽  
Temporal Logics ◽  
General Issue ◽  
Proof Systems

Howard Barringer was a pioneer in the study of temporal logics withfixpoints. Their addition adds considerable expressive power.One general issue is how to defineproof systems for such logics. Here we examine proof systems formodal logic with fixpoints. We present a tableau proof systemfor checking validity of formulaswhich uses names to keep track of unfoldings of fixpoint variables.

scholarly journals Complete proof systems for weighted modal logic

2014 ◽  
Vol 546 ◽  
pp. 164-175 ◽  
Author(s):  
Kim G. Larsen ◽  
Radu Mardare
Keyword(s):  
Modal Logic ◽  
Complete Proof ◽  
Proof Systems

Aristotle's modal logic

1995 ◽  
Author(s):  
Richard Patterson
Keyword(s):  
Modal Logic

Modal Logic

1980 ◽  
Author(s):  
Brian F. Chellas
Keyword(s):  
Modal Logic

Modality and folk psychology

2019 ◽  
Vol 28 (1) ◽  
pp. 19-27
Author(s):  
Ja. O. Petik
Keyword(s):  
Modal Logic ◽  
Brain Activity ◽  
Formal System ◽  
Philosophy Of Logic ◽  
Psychological States ◽  
Formal Systems ◽  
Modern Psychology ◽  
Philosophical Interpretation ◽  
Important Direction

The connection of the modern psychology and formal systems remains an important direction of research. This paper is centered on philosophical problems surrounding relations between mental and logic. Main attention is given to philosophy of logic but certain ideas are introduced that can be incorporated into the practical philosophical logic. The definition and properties of basic modal logic and descending ones which are used in study of mental activity are in view. The defining role of philosophical interpretation of modality for the particular formal system used for research in the field of psychological states of agents is postulated. Different semantics of modal logic are studied. The hypothesis about the connection of research in cognitive psychology (semantics of brain activity) and formal systems connected to research of psychological states is stated.

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