Horn fragments of the Halpern-Shoham interval temporal logic
We investigate the satisfiability problem for Horn fragments of the Halpern-Shoham interval temporal logic depending on the type (box or diamond) of the interval modal operators, the type of the underlying linear order (discrete or dense), and the type of semantics for the interval relations (reflexive or irreflexive). For example, we show that satisfiability of Horn formulas with diamonds is undecidable for any type of linear orders and semantics. On the contrary, satisfiability of Horn formulas with boxes is tractable over both discrete and dense orders under the reflexive semantics and over dense orders under the irreflexive semantics but becomes undecidable over discrete orders under the irreflexive semantics. Satisfiability of binary Horn formulas with both boxes and diamonds is always undecidable under the irreflexive semantics.
“Let's be Logical” is a double invitation. Although logic often refers to a disposition of mind that we all share, this disposition might be confused once its theoretical sources are questioned. The present volume offers thirteen articles that address various aspects of the discipline of logic and its methods, notably formalism, the theory of opposition, mathematical truth, and history of logic. This volume has been prepared with the pedagogical concern of making it accessible to a wide audience of logic and philosophy readers.
In this paper we prove that the derivability problems for product-free Lambek calculus and product-free Lambek calculus allowing empty premises are NP-complete. Also we introduce a new derivability characterization for these calculi.
The Markov School is the school of mathematics (mostly mathematical logic) arisen in St.Petersburg in the 20th century. Historically, the Markov School has been largely connected with the Steklov Mathematical Institute in St. Petersburg. Today, many Markov School mathematicians have taken up positions in different countries; of course, we do not attempt to restrict this survey only to those who have stayed in St. Petersburg. However, all mathematicians whose work we describe studied in St. Petersburg and, at least for several years and often for decades, worked at the Steklov Mathematical Institute. In this paper, we primarily discuss what has happened over the last two decades, so a certain bias to computational complexity is to be expected.
During his scientific life Albert Visser has contributed to a great variety of disciplines in logic, ranging from provability logics, interpretability, and formal arithmetic to philosophy, linguistics and formal language semantics. This Liber Amicorum is in honour of his long and distinguished career, and nicely bears tribe to the diversity of Albert Visser's interests. Filed with contributions from his colleagues, the book illustrates the important role thatAlbert Visser plays and has played as a logician in the Netherlands and abroad.
Predictive analysis gradually gains importance in industry. For instance, service engineers at Siemens diagnostic centres unveil hidden knowledge in huge amounts of historical sensor data and use it to improve the predictive systems analysing live data. Currently, the analysis is usually done using data-dependent rules that are specific to individual sensors and equipment. This dependence poses significant challenges in rule authoring, reuse, and maintenance by engineers. One solution to this problem is to employ ontology-based data access (OBDA), which provides a conceptual view of data via an ontology. However, classical OBDA systems do not support access to temporal data and reasoning over it. To address this issue, we propose a framework for temporal OBDA. In this framework, we use extended mapping languages to extract information about temporal events in the RDF format, classical ontology and rule languages to reflect static information, as well as a temporal rule language to describe events. We also propose a SPARQL-based query language for retrieving temporal information and, finally, an architecture of system implementation extending the state-of-the-art OBDA platform Ontop.
This article deals with the problem of translations. It covers the history of translation in linguistics and analyzes peculiarities and role of translation in logic. Moreover, the article contains typical examples of embedding operations in terms of dierent logical theories.