Natural deduction systems for classical, intuitionistic and modal logics were deeply investigated by Prawitz [D. Prawitz, Natural Deduction: A Proof-theoretical Study, in: Stockholm Studies in Philosophy, vol. 3, Almqvist and Wiksell, Stockholm, 1965. Reprinted at: Dover Publications, Dover Books on Mathematics, 2006] from a proof-theoretical perspective. Prawitz proved weak normalization for c...

The exogenous quantum propositional logic (EQPL) was proposed in [13, 14, 15] for modeling and reasoning about quantum systems, embodying all that is stated in the relevant postulates of quantum physics (as presented, for instance, in [9, 16]). The logic was designed from the semantics upwards, starting with the key idea of adopting superpositions of classical models as the models of the propos...

A tableau calculus constituting a decision procedure for hybrid logic with the converse modalities, the global ones and a restricted use of the binder has been defined in a previous paper. This work shows how to extend such a calculus to multi-modal logic equipped with two features largely used in description logics, i.e. transitivity and relation inclusion assertions. An implementation of the ...

This paper presents a general method for proving termination of tableaux-based procedures for modal-type logics and related firstorder fragments. The method is based on connections between filtration arguments and a general blocking technique. The method provides a general framework for developing tableau-based decision procedures for a large class of logics. In particular, the method can be ap...

1 Polynomials as proof devices Algebraic proof systems based on formal polynomials over algebraically closed fields (the “polynomial ring calculus”) were introduced in [9] (see [10] and [11] for recent developments). Formal polynomials work as a powerful tool for logical derivation in classical and non-classical logics, in particular for propositional many-valued logics, paraconsistent logics a...

We study elementary modal logics, i.e. modal logic considered over first-order definable classes of frames. The classical semantics of modal logic allows infinite structures, but often practical applications require to restrict our attention to finite structures. Many decidability and undecidability results for the elementary modal logics were proved separately for general satisfiability and fo...

First-order modal logics have many applications, e.g. in planning and program verification. Whereas comprehensive and standardized problem libraries exist for, e.g., classical (TPTP library) and intuitionistic (ILTP library) logic, nothing comparable is so far available for firstorder modal logics. The aim of the Quantified Modal Logic Theorem Proving (QMLTP) library is to close this gap by pro...

Discussive logics (also called discursive logics) were introduced in 1948 by Stanis law Jaśkowski and constitute the first family of formal paraconsistent logics. The basic mechanism behind discussive logics is as simple as ingenious. Where L is some modal logic and Γ♦ = {♦A | A ∈ Γ}, a discussive logic DL, associated with L, is obtained by specifying the language L of DL and by stipulating tha...