Optimal Tableaux Method for Constructive Satisfiability Testing and Model Synthesis in the Alternating-time Temporal Logic ATL+

We develop a sound, complete and practically implementable tableaux-based decision method for constructive satisfiability testing and model synthesis in the fragment ATL+ of the full Alternating time temporal logic ATL*. The method extends in an essential way a previously developed tableaux-based decision method for ATL and works in 2EXPTIME, which is the optimal worst case complexity of the satisfiability problem for ATL+ . We also discuss how suitable parametrizations and syntactic restrictions on the class of input ATL+ formulae can reduce the complexity of the satisfiability problem.Comment: 45 page

First-order Goedel logics

First-order Goedel logics are a family of infinite-valued logics where the sets of truth values V are closed subsets of [0, 1] containing both 0 and 1. Different such sets V in general determine different Goedel logics G_V (sets of those formulas which evaluate to 1 in every interpretation into V). It is shown that G_V is axiomatizable iff V is finite, V is uncountable with 0 isolated in V, or every neighborhood of 0 in V is uncountable. Complete axiomatizations for each of these cases are given. The r.e. prenex, negation-free, and existential fragments of all first-order Goedel logics are also characterized.Comment: 37 page

A hybrid logic for XML reference constraints

XML emerged as the (meta) mark-up language for representing, exchanging, and storing semistructured data. The structure of an XML document may be specified either through DTD (Document Type Definition) language or through the specific language XML Schema. While the expressiveness of XML Schema allows one to specify both the structure and constraints for XML documents, DTD does not allow the specification of integrity constraints for XML documents. On the other side, DTD has a very compact notation opposed to the complex notation and syntax of XML Schema. Thus, it becomes important to consider the issue of how to express further constraints on DTD-based XML documents, still retaining the simplicity and succinctness of DTDs. According to this scenario, in this paper we focus on a (as much as possible) simple logic, named XHyb, expressive enough to allow the specification of the most common integrity and reference constraints in XML documents. In particular, we focus on constraints on ID and IDREF(S) attributes, which are the common way of logically connecting parts of XML documents, besides the usual parent-child relationship of XML elements. Differently from other previously proposed hybrid logics, in XHyb IDREF(S) attributes are explicitly expressible by means of suitable syntactical constructors. Moreover, we propose a refinement of the usual graph representation of XML documents in order to represent XML documents in a formal and intuitive way without flatten accessibility through IDREF(S) to the usual parent-child relationship. Model checking algorithms are then proposed, to verify that a given XML document satisfies the considered constraints

Pseudo-contractions as Gentle Repairs

Updating a knowledge base to remove an unwanted consequence is a challenging task. Some of the original sentences must be either deleted or weakened in such a way that the sentence to be removed is no longer entailed by the resulting set. On the other hand, it is desirable that the existing knowledge be preserved as much as possible, minimising the loss of information. Several approaches to this problem can be found in the literature. In particular, when the knowledge is represented by an ontology, two different families of frameworks have been developed in the literature in the past decades with numerous ideas in common but with little interaction between the communities: applications of AGM-like Belief Change and justification-based Ontology Repair. In this paper, we investigate the relationship between pseudo-contraction operations and gentle repairs. Both aim to avoid the complete deletion of sentences when replacing them with weaker versions is enough to prevent the entailment of the unwanted formula. We show the correspondence between concepts on both sides and investigate under which conditions they are equivalent. Furthermore, we propose a unified notation for the two approaches, which might contribute to the integration of the two areas

Internal Calculi for Separation Logics

We present a general approach to axiomatise separation logics with heaplet semantics with no external features such as nominals/labels. To start with, we design the first (internal) Hilbert-style axiomatisation for the quantifier-free separation logic SL(?, -*). We instantiate the method by introducing a new separation logic with essential features: it is equipped with the separating conjunction, the predicate ls, and a natural guarded form of first-order quantification. We apply our approach for its axiomatisation. As a by-product of our method, we also establish the exact expressive power of this new logic and we show PSpace-completeness of its satisfiability problem

A decidable weakening of Compass Logic based on cone-shaped cardinal directions

We introduce a modal logic, called Cone Logic, whose formulas describe properties of points in the plane and spatial relationships between them. Points are labelled by proposition letters and spatial relations are induced by the four cone-shaped cardinal directions. Cone Logic can be seen as a weakening of Venema's Compass Logic. We prove that, unlike Compass Logic and other projection-based spatial logics, its satisfiability problem is decidable (precisely, PSPACE-complete). We also show that it is expressive enough to capture meaningful interval temporal logics - in particular, the interval temporal logic of Allen's relations "Begins", "During", and "Later", and their transposes