Related papers: Finitary semantics of linear logic and higher-orde…

Real-valued logics have seen a renewed interest in verification for probabilistic and quantitative systems, in particular machine learning models, where they can be used to directly integrate specifications in the training objective. To do…

Machine learning algorithms enable advanced decision making in contemporary intelligent systems. Research indicates that there is a tradeoff between their model performance and explainability. Machine learning models with higher performance…

We explore the fundamental problem of sorting through the lens of learning-augmented algorithms, where algorithms can leverage possibly erroneous predictions to improve their efficiency. We consider two different settings: In the first…

First-order linear temporal logic (FOLTL) is a flexible and expressive formalism capable of naturally describing complex behaviors and properties. Although the logic is in general highly undecidable, the idea of using it as a specification…

The parameterized model-checking problem for a class of first-order sentences (queries) asks to decide whether a given sentence from the class holds true in a given relational structure (database); the parameter is the length of the…

We present a unified categorical treatment of completeness theorems for several classical and intuitionistic infinitary logics with a proposed axiomatization. This provides new completeness theorems and subsumes previous ones by G\"odel,…

Combinatory logic shows that bound variables can be eliminated without loss of expressiveness. It has applications both in the foundations of mathematics and in the implementation of functional programming languages. The original…

Tractability results for the model checking problem of logics yield powerful algorithmic meta theorems of the form: Every computational problem expressible in a logic $L$ can be solved efficiently on every class $\mathscr{C}$ of structures…

A semantical embedding of input/output logic in classical higher-order logic is presented. This embedding enables the mechanisation and automation of reasoning tasks in input/output logic with off-the-shelf higher-order theorem provers and…

Model checking is an automatic formal verification technique that is widely used in hardware verification. The state-of-the-art complete model-checking techniques, based on IC3/PDR and its general variant CAR, are based on computing…

First-order model counting (FOMC) is a computational problem that asks to count the models of a sentence in finite-domain first-order logic. In this paper, we argue that the capabilities of FOMC algorithms to date are limited by their…

Logical relations constitute a key method for reasoning about contextual equivalence of programs in higher-order languages. They are usually developed on a per-case basis, with a new theory required for each variation of the language or of…

Sets with atoms serve as an alternative to ZFC foundations for mathematics, where some infinite, though highly symmetric sets, behave in a finitistic way. Therefore, one can try to carry over analysis of the classical algorithms from finite…

A cyclic proof system allows us to perform inductive reasoning without explicit inductions. We propose a cyclic proof system for HFLN, which is a higher-order predicate logic with natural numbers and alternating fixed-points. Ours is the…

This paper is motivated by the theory of sequential dynamical systems, developed as a basis for a mathematical theory of computer simulation. It contains a classification of finite dynamical systems on binary strings, which are obtained by…

Over the past two decades several fragments of first-order logic have been identified and shown to have good computational and algorithmic properties, to a great extent as a result of appropriately describing the image of the standard…

In this paper, we compare two alternative mechanisms for deciding the validity of first-order formulas over finite domains supported by the mathematical model checker RISCAL: first, the original approach of semantic evaluation (based on an…

We investigate quantifier alternation hierarchies in first-order logic on finite words. Levels in these hierarchies are defined by counting the number of quantifier alternations in formulas. We prove that one can decide membership of a…

The problem if a given configuration of a pushdown automaton (PDA) is bisimilar with some (unspecified) finite-state process is shown to be decidable. The decidability is proven in the framework of first-order grammars, which are given by…

This note further addresses the global optimization problem for max-plus linear systems considered in [Automatica 119 (2020) 109104]. Firstly, the operations between infinity elemens and real numbers involved in the formulas of solving…