Related papers: Computational Coverage of TLG: Nonlinearity
This paper presents a range of quantitative extensions for the temporal logic CTL. We enhance temporal modalities with the ability to constrain the number of states satisfying certain sub-formulas along paths. By selecting the combinations…
Regular tree grammars and regular path expressions constitute core constructs widely used in programming languages and type systems. Nevertheless, there has been little research so far on frameworks for reasoning about path expressions…
This paper introduces two sequent calculi for intuitionistic strong L\"ob logic ${\sf iSL}_\Box$: a terminating sequent calculus ${\sf G4iSL}_\Box$ based on the terminating sequent calculus ${\sf G4ip}$ for intuitionistic propositional…
Relation-changing modal logics are extensions of the basic modal logic that allow changes to the accessibility relation of a model during the evaluation of a formula. In particular, they are equipped with dynamic modalities that are able to…
Non-deterministic constraint logic (NCL) is a simple model of computation based on orientations of a constraint graph with edge weights and vertex demands. NCL captures \PSPACE\xspace and has been a useful tool for proving algorithmic…
The cut-elimination procedure for the provability logic is known to be problematic: a L\"ob-like rule keeps cut-formulae intact on reduction, even in the principal case, thereby complicating the proof of termination. In this paper, we…
Datalog is one of the best-known rule-based languages, and extensions of it are used in a wide context of applications. An important Datalog extension is Disjunctive Datalog, which significantly increases the expressivity of the basic…
We introduce a linear infinitary $\lambda$-calculus, called $\ell\Lambda_{\infty}$, in which two exponential modalities are available, the first one being the usual, finitary one, the other being the only construct interpreted…
We extend first-order logic with counting by a new operator that allows it to formalise a limited form of recursion which can be evaluated in logarithmic space. The resulting logic LREC has a data complexity in LOGSPACE, and it defines…
Linear algebra algorithms often require some sort of iteration or recursion as is illustrated by standard algorithms for Gaussian elimination, matrix inversion, and transitive closure. A key characteristic shared by these algorithms is that…
To appear in Theory and Practice of Logic Programming (TPLP). In this paper we propose an extension of logic programming (LP) where each default literal derived from the well-founded model is associated to a justification represented as an…
Non-classical negations may fail to be contradictory-forming operators in more than one way, and they often fail also to respect fundamental meta-logical properties such as the replacement property. Such drawbacks are witnessed by intricate…
We consider tensor grammars, which are an example of \commutative" grammars, based on the classical (rather than intuitionistic) linear logic. They can be seen as a surface representation of abstract categorial grammars ACG in the sense…
The categorical models of the differential lambda-calculus are additive categories because of the Leibniz rule which requires the summation of two expressions. This means that, as far as the differential lambda-calculus and differential…
Cumulative logics are studied in an abstract setting, i.e., without connectives, very much in the spirit of Makinson's early work. A powerful representation theorem characterizes those logics by choice functions that satisfy a weakening of…
Analyzing relational languages by their logical expressiveness is well understood. Something not well understood or even formalized is the vague concept of relational query patterns. What are query patterns? And how can we reason about…
Infinitesimal contraction analysis provides exponential convergence rates between arbitrary pairs of trajectories of a system by studying the system's linearization. An essentially equivalent viewpoint arises through stability analysis of a…
It is known that Metric Temporal Logic (MTL) is strictly less expressive than the Monadic First-Order Logic of Order and Metric (FO[<, +1]) when interpreted over timed words; this remains true even when the time domain is bounded a priori.…
We classify the complexity of the satisfiability problem for extensions of CTL and UB. The extensions we consider are Boolean combinations of path formulas, fairness properties, past modalities, and forgettable past. Our main result shows…
We aim at improving reasoning on inconsistent and uncertain data. We focus on knowledge-graph data, extended with time intervals to specify their validity, as regularly found in historical sciences. We propose principles on semantics for…