Cut-Free Gentzen Sequent Calculi for Tense Logics

Sequent Calculi for Nominal Tense Logics: A Step Towards Mechanization?

We define sequent-style calculi for nominal tense logics characterized by classes of modal frames that are first-order definable by certain Π 1 -formulae and Π 0 2 -formulae. The calculi are based on d’Agostino and Mondadori’s calculus KE and therefore they admit a restricted cutrule that is not eliminable. A nice computational property of the restriction is, for instance, that at any stage of ...

Cut - free Display Calculi for Nominal Tense

We deene cut-free display calculi for nominal tense logics extending the minimal nominal tense logic (MNTL) by addition of primitive axioms. To do so, we use a translation of MNTL into the minimal tense logic of inequality (MTL6 =) which is known to be properly displayable by application of Kracht's results. The rules of the display calculus MNTL for MNTL mimic those of the display calculus MTL...

Duplication-Free Tableau Calculi Together With Cut-Free and Contraction-Free Sequent Calculi for the Interpolable . . .

Graphical Sequent Calculi for Modal Logics

The syntax of modal graphs is defined in terms of the continuous cut and broken cut following Charles Peirce’s notation in the gamma part of his graphical logic of existential graphs. Graphical calculi for normal modal logics are developed based on a reformulation of the graphical calculus for classical propositional logic. These graphical calculi are of the nature of deep inference. The relati...

Sequent Calculi for Indexed Epistemic Logics

Indexed epistemic logics constitute a well-structured class of quantified epistemic logics with great expressive power and a well-behaved semantics based on the notion of epistemic transition model. It follows that they generalize term-modal logics. As to proof theory, the only axiomatic system for which we have a completeness theorem is the minimal system Q.Ke, whether with classical or with f...