Expressive Logical Combinators for Free

International audienceA popular technique for the analysis of web query languages relies on the translation of queries into logical formulas. These formulas are then solved for satisfiability using an off-the-shelf satisfiabil-ity solver. A critical aspect in this approach is the size of the obtained logical formula, since it constitutes a factor that affects the combined complexity of the global approach. We present logical combi-nators whose benefit is to provide an exponential gain in succinctness in terms of the size of the logical representation. This opens the way for solving a wide range of problems such as satisfiability and containment for expressive query languages in exponential-time, even though their direct formulation into the underlying logic results in an exponential blowup of the formula size, yielding an incorrectly presumed two-exponential time complexity. We illustrate this from a practical point of view on a few examples such as numerical occurrence constraints and tree frontier properties which are concrete problems found with semi-structured data

Expressiveness of a spatial logic for trees

International audienceIn this paper we investigate the quantifier-free fragment of the TQL logic proposed by Cardelli and Ghelli. The TQL logic, inspired from the ambient logic, is the core of a query language for semistructured data represented as unranked and unordered trees. The fragment we consider here, named STL, contains as main features spatial composition and location as well as a fixed point construct. We prove that satisfiability for STL is undecidable.We show also that STL is strictly more expressive that the Presburger monadic second-order logic (PMSO) of Seidl, Schwentick and Muscholl when interpreted over unranked and unordered edge-labeled trees. We define a class of tree automata whose transitions are conditioned by arithmetical constraints; we show then how to compute from a closed STL formula a tree automaton accepting precisely the models of the formula. Finally, still using our tree automata framework, we exhibit some syntactic restrictions over STL formulae that allow us to capture precisely the logics MSO and PMSO

On Decision Procedures for Ordered Collections

We describe a decision procedure for a logic that supports 1) finite collections of elements (sets or multisets), 2) the cardinality operator, 3) a total order relation on elements, and 4) min and max operators on entire collections. Among the applications of this logic are 1) reasoning about the externally observable behavior of data structures such as random access priority queues, 2) specifying witness functions for synthesis problems of set algebra, and 3) reasoning about constraints on orderings arising in termination proofs

The Fine-Grained Complexity of Problems Expressible by First-Order Logic and Its Extensions

This dissertation studies the fine-grained complexity of model checking problems for fixed logical formulas on sparse input structures. The Orthogonal Vectors problem is an important and well-studied problem in fine-grained complexity: its hardness is implied by the Strong Exponential Time Hypothesis, and its hardness implies the hardness of many other interesting problems. We show that the Orthogonal Vectors problem is complete in the class of first-order model checking on sparse structures, under fine-grained reductions. In other words, the hardness of Orthogonal Vectors and the hardness of first-order model checking imply each other. This also gives us an improved algorithm for first-order model checking problems. Among all first-order logic formulas in prenex normal form, we have reasons to believe that quantifier structures $\exists \dots \exists \forall$ and $\forall \dots \forall \exists$ may be the hardest in computational complexity: If the Nondeterministic version of the Strong Exponential Time Hypothesis is true, formulas of these forms are the only hard ones under the Strong Exponential Time Hypothesis. We can add extensions to first-order logic to strengthen its expressive power. This work also studies the fine-grained complexity of first-order formulas with comparison on structures with total order, first-order formulas with transitive closure operations, first-order formulas of fixed quantifier rank, and first-order formulas of fixed variable complexity. We also introduce a technique that can be used to reduce from sequential problems on graphs to parallel problems on sets, which can be applied to extending the Least Weight Subsequence problems from linear structures to some special classes of graphs

Karp-Miller Trees for a Branching Extension of VASS

We study BVASS (Branching VASS) which extend VASS (Vector Addition Systems with States) by allowing addition transitions that merge two configurations. Runs in BVASS are tree-like structures instead of linear ones as for VASS. We show that the construction of Karp-Miller trees for VASS can be extended to BVASS. This entails that the coverability set for BVASS is computable. This allows us to obtain decidability results for certain classes of equational tree automata with an associative-commutative symbol. Recent independent work by de Groote et al. implies that decidability of reachability in BVASS is equivalent to decidability of provability in MELL (multiplicative exponential linear logic), which is still an open problem. Hence our results are also a step towards answering this question in the affirmative

LIPIcs, Volume 248, ISAAC 2022, Complete Volume

LIPIcs, Volume 248, ISAAC 2022, Complete Volum

LIPIcs, Volume 261, ICALP 2023, Complete Volume

LIPIcs, Volume 261, ICALP 2023, Complete Volum

Form and formalism in linguistics

"Form" and "formalism" are a pair of highly productive and polysemous terms that occupy a central place in much linguistic scholarship. Diverse notions of "form" – embedded in biological, cognitive and aesthetic discourses – have been employed in accounts of language structure and relationship, while "formalism" harbours a family of senses referring to particular approaches to the study of language as well as representations of linguistic phenomena. This volume brings together a series of contributions from historians of science and philosophers of language that explore some of the key meanings and uses that these multifaceted terms and their derivatives have found in linguistics, and what these reveal about the mindset, temperament and daily practice of linguists, from the nineteenth century up to the present day