461 research outputs found
Schematic Cut elimination and the Ordered Pigeonhole Principle [Extended Version]
In previous work, an attempt was made to apply the schematic CERES method [8]
to a formal proof with an arbitrary number of {\Pi} 2 cuts (a recursive proof
encapsulating the infinitary pigeonhole principle) [5]. However the derived
schematic refutation for the characteristic clause set of the proof could not
be expressed in the formal language provided in [8]. Without this formalization
a Herbrand system cannot be algorithmically extracted. In this work, we provide
a restriction of the proof found in [5], the ECA-schema (Eventually Constant
Assertion), or ordered infinitary pigeonhole principle, whose analysis can be
completely carried out in the framework of [8], this is the first time the
framework is used for proof analysis. From the refutation of the clause set and
a substitution schema we construct a Herbrand system.Comment: Submitted to IJCAR 2016. Will be a reference for Appendix material in
that paper. arXiv admin note: substantial text overlap with arXiv:1503.0855
Completeness of a first-order temporal logic with time-gaps
The first-order temporal logics with □ and ○ of time structures isomorphic to ω (discrete linear time) and trees of ω-segments (linear time with branching gaps) and some of its fragments are compared: the first is not recursively axiomatizable. For the second, a cut-free complete sequent calculus is given, and from this, a resolution system is derived by the method of Maslov
Incompleteness of a first-order Gödel logic and some temporal logics of programs
It is shown that the infinite-valued first-order Gödel logic G° based on the set of truth values {1/k: k ε w {0}} U {0} is not r.e. The logic G° is the same as that obtained from the Kripke semantics for first-order intuitionistic logic with constant domains and where the order structure of the model is linear. From this, the unaxiomatizability of Kröger's temporal logic of programs (even of the fragment without the nexttime operator O) and of the authors' temporal logic of linear discrete time with gaps follows
Introducing Quantified Cuts in Logic with Equality
Cut-introduction is a technique for structuring and compressing formal
proofs. In this paper we generalize our cut-introduction method for the
introduction of quantified lemmas of the form (for
quantifier-free ) to a method generating lemmas of the form . Moreover, we extend the original method to predicate
logic with equality. The new method was implemented and applied to the TSTP
proof database. It is shown that the extension of the method to handle equality
and quantifier-blocks leads to a substantial improvement of the old algorithm
Ontology-Based Data Access and Integration
An ontology-based data integration (OBDI) system is an information management system consisting of three components: an ontology, a set of data sources, and the mapping between the two. The ontology is a conceptual, formal description of the domain of interest to a given organization (or a community of users), expressed in terms of relevant concepts, attributes of concepts, relationships between concepts, and logical assertions characterizing the domain knowledge. The data sources are the repositories accessible by the organization where data concerning the domain are stored. In the general case, such repositories are numerous, heterogeneous, each one managed and maintained independently from the others. The mapping is a precise specification of the correspondence between the data contained in the data sources and the elements of the ontology. The main purpose of an OBDI system is to allow information consumers to query the data using the elements in the ontology as predicates.
In the special case where the organization manages a single data source, the term ontology-based data access (ODBA) system is used
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