Lower complexity bounds in justification logic

Justification Logic studies epistemic and provability phenomena by introducing justifications/proofs into the language in the form of justification terms. Pure justification logics serve as counterparts of traditional modal epistemic logics, and hybrid logics combine epistemic modalities with justification terms. The computational complexity of pure justification logics is typically lower than that of the corresponding modal logics. Moreover, the so-called reflected fragments, which still contain complete information about the respective justification logics, are known to be in~NP for a wide range of justification logics, pure and hybrid alike. This paper shows that, under reasonable additional restrictions, these reflected fragments are NP-complete, thereby proving a matching lower bound. The proof method is then extended to provide a uniform proof that the corresponding full pure justification logics are $\Pi^p_2$-hard, reproving and generalizing an earlier result by Milnikel.

A Finite Model Property for Gödel Modal Logics

A new semantics with the finite model property is provided and used to establish decidability for Gödel modal logics based on (crisp or fuzzy) Kripke frames combined locally with Gödel logic. A similar methodology is also used to establish decidability, and indeed co-NP-completeness for a Gödel S5 logic that coincides with the one-variable fragment of first-order Gödel logic.

Justifying induction on modal μ-formulae

We define a rank function for formulae of the propositional modal μ-calculus such that the rank of a fixed point is strictly bigger than the rank of any of its finite approximations. A rank function of this kind is needed, for instance, to establish the collapse of the modal μ-hierarchy over transitive transition systems. We show that the range of the rank function is ωω. Further we establish that the rank is computable by primitive recursion, which gives us a uniform method to generate formulae of arbitrary rank below ωω.

Modal interpolation via nested sequents

The main method of proving the Craig Interpolation Property (CIP) constructively uses cut-free sequent proof systems. Until now, however, no such method has been known for proving the CIP using more general sequent-like proof formalisms, such as hypersequents, nested sequents, and labelled sequents. In this paper, we start closing this gap by presenting an algorithm for proving the CIP for modal logics by induction on a nested-sequent derivation. This algorithm is applied to all the logics of the so-called modal cube.

Applying logic forms and statistical methods to CL-SR performance

This paper describes a CL-SR system that employs two different techniques: the first one is based on NLP rules that consist on applying logic forms to the topic processing while the second one basically consists on applying the IR-n statistical search engine to the spoken document collection. The application of logic forms to the topics allows to increase the weight of topic terms according to a set of syntactic rules. Thus, the weights of the topic terms are used by IR-n system in the information retrieval process.

On the relative complexity of labelled modal tableaux

We investigate the relative complexity of two free-variable labelled modal tableaux(KEM and Single Step Tableaux, SST). We discuss the reasons why p-simulation is not a proper measure of the relative complexity of tableaux-like proof systems, and we propose an improved comparison scale (p-search-simulation). Finally we show that KEM p-search-simulates SST while SST cannot p-search-simulate KEM.