Most of the sequent/tableau based proof systems for the modal logic S4 need to duplicate formulas and thus are required to adopt some method of loop checking [7, 13, 10]. In what follows we present a tableau-like proof system for S4, based on D’Agostino and Mondadori’s classical KE [3], which is free of duplication and loop checking. The key feature of this system (let us call it KES4) consists...

For the verificationist principle of truth underlying intuitionistic logic and constructivism, semantic truth conditions for propositions are substituted by syntactically defined assertion conditions for judgments ([2]). Where the standard interpretation of such notion of truth is given in a language for arithmetic, far less clear is how to interpret it for the representation of rational knowle...

We introduce distributive unimodal logic as a modal logic of binary relations over posets which naturally generalizes the classical modal logic of binary relations over sets. The relational semantics of this logic is similar to the relational semantics of intuitionistic modal logic and positive modal logic, but it generalizes both of these by placing no restrictions on the accessibility relatio...

For the model of probabilistic labelled transition systems that allow for the co-existence of nondeterminism and probabilities, we present two notions of bisimulation metrics: one is state-based and the other is distribution-based. We provide a sound and complete modal characterisation for each of them, using real-valued modal logics based on the Hennessy-Milner logic. The logic for characteris...

We compare the expressiveness of the fragments of Halpern and Shoham’s interval logic (HS), i.e., of all interval logics with modal operators associated with Allen’s relations between intervals in linear orders. We establish a complete set of interdefinability equations between these modal operators, and thus obtain a complete classification of the family of 2 fragments of HS with respect to th...

4 Literature review 8 4.1 Modal and Temporal Logics . . . . . . . . . . . . . . . . . . . . . . . . . . 8 4.2 Games for Modal and Temporal Logics . . . . . . . . . . . . . . . . . . . . 9 4.3 Models of Concurrency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 4.4 Games for Models of Concurrency . . . . . . . . . . . . . . . . . . . . . . 10 4.5 Lattices and Complete lattices . . ....

I introduce now for the first time the neutrosophic modal logic. The Neutrosophic Modal Logic includes the neutrosophic operators that express the modalities. It is an extension of neutrosophic predicate logic, and of neutrosophic propositional logic. In order for the paper to be self-contained, I also recall the etymology and definition of neutrosophy and of neutrosophic logic. Several example...

We consider propositional modal logic with two modal operators and [ 6 =]. In topological semantics is interpreted as an interior operator and [ 6=] as difference. We show that some important topological properties are expressible in this language. In addition, we present a few logics and proofs of f.m.p. and of completeness theorems.

In this paper, reasoning methods for the interval-based modal temporal logic LLP which employs the modal operators sometimes, always, next, and chop are described. A constraint deduction approach is proposed and compared with a sequent calculus which has been developed as the basic machinery for the deductive planning system PHI which uses LLP as underlying formalism.

We introduce a new order-topological semantics for the positive modal mu-calculus over modal compact Hausdorff spaces, which are generalizations of descriptive frames. We define Sahlqvist sequents in this language, prove Esakia’s lemma and Sahlqvist preservation theorem for this semantics. We show that every Sahlqvist sequent has a frame correspondent in first-order logic with fixed-point opera...