Conservative Extensions in Guarded and Two-Variable Fragments

We investigate the decidability and computational complexity of (deductive) conservative extensions in fragments of first-order logic (FO), with a focus on the two-variable fragment FO$^2$ and the guarded fragment GF. We prove that conservative extensions are undecidable in any FO fragment that contains FO$^2$ or GF (even the three-variable fragment thereof), and that they are decidable and 2\ExpTime-complete in the intersection GF$^2$ of FO$^2$ and GF

Conservative Extensions and Satisfiability in Fragments of First-Order Logic : Complexity and Expressive Power

In this thesis, we investigate the decidability and computational complexity of (deductive) conservative extensions in expressive fragments of first-order logic, such as two-variable and guarded fragments. Moreover, we also investigate the complexity of (query) conservative extensions in Horn description logics with inverse roles. Aditionally, we investigate the computational complexity of the satisfiability problem in the unary negation fragment of first-order logic extended with regular path expressions. Besides complexity results, we also study the expressive power of relation-changing modal logics. In particular, we provide translations intto hybrid logic and compare their expressive power using appropriate notions of bisimulations

Deciding regular grammar logics with converse through first-order logic

We provide a simple translation of the satisfiability problem for regular grammar logics with converse into GF2, which is the intersection of the guarded fragment and the 2-variable fragment of first-order logic. This translation is theoretically interesting because it translates modal logics with certain frame conditions into first-order logic, without explicitly expressing the frame conditions. A consequence of the translation is that the general satisfiability problem for regular grammar logics with converse is in EXPTIME. This extends a previous result of the first author for grammar logics without converse. Using the same method, we show how some other modal logics can be naturally translated into GF2, including nominal tense logics and intuitionistic logic. In our view, the results in this paper show that the natural first-order fragment corresponding to regular grammar logics is simply GF2 without extra machinery such as fixed point-operators.Comment: 34 page

Lewis meets Brouwer: constructive strict implication

C. I. Lewis invented modern modal logic as a theory of "strict implication". Over the classical propositional calculus one can as well work with the unary box connective. Intuitionistically, however, the strict implication has greater expressive power than the box and allows to make distinctions invisible in the ordinary syntax. In particular, the logic determined by the most popular semantics of intuitionistic K becomes a proper extension of the minimal normal logic of the binary connective. Even an extension of this minimal logic with the "strength" axiom, classically near-trivial, preserves the distinction between the binary and the unary setting. In fact, this distinction and the strong constructive strict implication itself has been also discovered by the functional programming community in their study of "arrows" as contrasted with "idioms". Our particular focus is on arithmetical interpretations of the intuitionistic strict implication in terms of preservativity in extensions of Heyting's Arithmetic.Comment: Our invited contribution to the collection "L.E.J. Brouwer, 50 years later

Lindstrom theorems for fragments of first-order logic

Lindstr\"om theorems characterize logics in terms of model-theoretic conditions such as Compactness and the L\"owenheim-Skolem property. Most existing characterizations of this kind concern extensions of first-order logic. But on the other hand, many logics relevant to computer science are fragments or extensions of fragments of first-order logic, e.g., k-variable logics and various modal logics. Finding Lindstr\"om theorems for these languages can be challenging, as most known techniques rely on coding arguments that seem to require the full expressive power of first-order logic. In this paper, we provide Lindstr\"om theorems for several fragments of first-order logic, including the k-variable fragments for k>2, Tarski's relation algebra, graded modal logic, and the binary guarded fragment. We use two different proof techniques. One is a modification of the original Lindstr\"om proof. The other involves the modal concepts of bisimulation, tree unraveling, and finite depth. Our results also imply semantic preservation theorems.Comment: Appears in Logical Methods in Computer Science (LMCS

Program Transformations for Asynchronous and Batched Query Submission

The performance of database/Web-service backed applications can be significantly improved by asynchronous submission of queries/requests well ahead of the point where the results are needed, so that results are likely to have been fetched already when they are actually needed. However, manually writing applications to exploit asynchronous query submission is tedious and error-prone. In this paper we address the issue of automatically transforming a program written assuming synchronous query submission, to one that exploits asynchronous query submission. Our program transformation method is based on data flow analysis and is framed as a set of transformation rules. Our rules can handle query executions within loops, unlike some of the earlier work in this area. We also present a novel approach that, at runtime, can combine multiple asynchronous requests into batches, thereby achieving the benefits of batching in addition to that of asynchronous submission. We have built a tool that implements our transformation techniques on Java programs that use JDBC calls; our tool can be extended to handle Web service calls. We have carried out a detailed experimental study on several real-life applications, which shows the effectiveness of the proposed rewrite techniques, both in terms of their applicability and the performance gains achieved.Comment: 14 page