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Differential Linear Logic enriches Linear Logic with additional logical rules for the exponential connectives, dual to the usual rules of dereliction, weakening and contraction. We present a proof-net syntax for Differential Linear Logic…
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…
The present paper constructs three new systems of clarithmetic (arithmetic based on computability logic --- see http://www.cis.upenn.edu/~giorgi/cl.html): CLA8, CLA9 and CLA10. System CLA8 is shown to be sound and extensionally complete…
A new technique is presented to prove non-termination of term rewriting. The basic idea is to find a non-empty regular language of terms that is closed under rewriting and does not contain normal forms. It is automated by representing the…
Large language models (LLMs) have achieved remarkable multi-step reasoning capabilities across various domains. However, LLMs still face distinct challenges in complex logical reasoning, as (1) proof-finding requires systematic exploration…
Proving linearizability of concurrent data structures remains a key challenge for verification. We present temporal interpolation as a new proof principle to conduct such proofs using hindsight arguments within concurrent separation logic.…
We study several extensions of linear-time and computation-tree temporal logics with quantifiers that allow for counting how often certain properties hold. For most of these extensions, the model-checking problem is undecidable, but we show…
Recently it was shown that it is undecidable whether a term rewrite system can be proved terminating by a polynomial interpretation in the natural numbers. In this paper we show that this is also the case when restricting the…
We present a novel asynchronous hyper linear time temporal logic named LPrL (Linear Time Predicate Logic) and establish its basic theory. LPrL is a natural first order extension of LTL (Linear time temporal logic), in which the predicates…
There are two kinds of approaches for termination analysis of logic programs: "transformational" and "direct" ones. Direct approaches prove termination directly on the basis of the logic program. Transformational approaches transform a…
Max-Plus Linear (MPL) systems are an algebraic formalism with practical applications in transportation networks, manufacturing and biological systems. In this paper, we investigate the problem of automatically analyzing the properties of…
Defeasible logic is a rule-based nonmonotonic logic, with both strict and defeasible rules, and a priority relation on rules. We show that inference in the propositional form of the logic can be performed in linear time. This contrasts…
We investigate infinitary wellfounded systems for linear logic with fixed points, with transfinite branching rules indexed by some closure ordinal $\alpha$ for fixed points. Our main result is that provability in the system for some…
In this paper we consider the specification and verification of infinite-state systems using temporal logic. In particular, we describe parameterised systems using a new variety of first-order temporal logic that is both powerful enough for…
The polylogarithmic time hierarchy structures sub-linear time complexity. In recent work it was shown that all classes $\tilde{\Sigma}_{m}^{\mathit{plog}}$ or $\tilde{\Pi}_{m}^{\mathit{plog}}$ ($m \in \mathbb{N}$) in this hierarchy can be…
Our goal is to answer elementary-level science questions using knowledge extracted automatically from science textbooks, expressed in a subset of first-order logic. Given the incomplete and noisy nature of these automatically extracted…
It is widely accepted that every system should be robust in that ``small'' violations of environment assumptions should lead to ``small'' violations of system guarantees, but it is less clear how to make this intuition mathematically…
In this paper we present an algorithm for performing runtime verification of a bounded temporal logic over timed runs. The algorithm consists of three elements. First, the bounded temporal formula to be verified is translated into a monadic…
While reachability analysis is one of the most promising approaches for formal verification of dynamic systems, a major disadvantage preventing a more widespread application is the requirement to manually tune algorithm parameters such as…
We provide a new realisability model based on orthogonality for the multiplicative fragment of linear logic, both in presence of generalised axioms (MLL*) and in the standard case (MLL). The novelty is the definition of cut elimination for…