Sequent Calculi for Multi-modal Logic with Interaction

2013 ◽  
pp. 124-134 ◽  
Author(s):  
Norbert Gratzl
Keyword(s):  
Modal Logic ◽  
Sequent Calculi

scholarly journals A general proof certification framework for modal logic

2019 ◽  
Vol 29 (8) ◽  
pp. 1344-1378
Author(s):  
TOMER LIBAL ◽  
MARCO VOLPE
Keyword(s):  
Modal Logic ◽  
General Framework ◽  
Sequent Calculus ◽  
Specification Language ◽  
Sequent Calculi ◽  
General Proof ◽  
Theorem Provers ◽  
Different Sources

One of the main issues in proof certification is that different theorem provers, even when designed for the same logic, tend to use different proof formalisms and produce outputs in different formats. The project ProofCert promotes the usage of a common specification language and of a small and trusted kernel in order to check proofs coming from different sources and for different logics. By relying on that idea and by using a classical focused sequent calculus as a kernel, we propose here a general framework for checking modal proofs. We present the implementation of the framework in a Prolog-like language and show how it is possible to specialize it in a simple and modular way in order to cover different proof formalisms, such as labelled systems, tableaux, sequent calculi and nested sequent calculi. We illustrate the method for the logic K by providing several examples and discuss how to further extend the approach.

Displaying the modal logic of consistency

1999 ◽  
Vol 64 (4) ◽  
pp. 1573-1590 ◽  
Author(s):  
Heinrich Wansing
Keyword(s):  
Modal Logic ◽  
Base System ◽  
Sequent Calculi

AbstractIt is shown that the constructive four-valued logic N4 can be faithfully embedded into the modal logic S4. This embedding is used to obtain complete, cut-free display sequent calculi for N4 and C4, the modal logic of consistency over N4. C4 is a natural monotonic base system for semantics-based non-monotonic reasoning.

scholarly journals POSITIVE LOGIC WITH ADJOINT MODALITIES: PROOF THEORY, SEMANTICS, AND REASONING ABOUT INFORMATION

2010 ◽  
Vol 3 (3) ◽  
pp. 351-373 ◽  
Author(s):  
MEHRNOOSH SADRZADEH ◽  
ROY DYCKHOFF
Keyword(s):  
Modal Logic ◽  
Multiagent Systems ◽  
Epistemic Logic ◽  
Proof Theory ◽  
Sequent Calculus ◽  
Dynamic Epistemic Logic ◽  
Algebraic Semantics ◽  
Sequent Calculi ◽  
Closure Operators ◽  
Positive Logic

We consider a simple modal logic whose nonmodal part has conjunction and disjunction as connectives and whose modalities come in adjoint pairs, but are not in general closure operators. Despite absence of negation and implication, and of axioms corresponding to the characteristic axioms of (e.g.) T, S4, and S5, such logics are useful, as shown in previous work by Baltag, Coecke, and the first author, for encoding and reasoning about information and misinformation in multiagent systems. For the propositional-only fragment of such a dynamic epistemic logic, we present an algebraic semantics, using lattices with agent-indexed families of adjoint pairs of operators, and a cut-free sequent calculus. The calculus exploits operators on sequents, in the style of “nested” or “tree-sequent” calculi; cut-admissibility is shown by constructive syntactic methods. The applicability of the logic is illustrated by reasoning about the muddy children puzzle, for which the calculus is augmented with extra rules to express the facts of the muddy children scenario.

scholarly journals Uniform interpolation and sequent calculi in modal logic

2018 ◽  
Vol 58 (1-2) ◽  
pp. 155-181 ◽  
Author(s):  
Rosalie Iemhoff
Keyword(s):  
Modal Logic ◽  
Sequent Calculi ◽  
Uniform Interpolation

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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