Related papers: FO-Complete Program Verification for Heap Logics
We show that if we enrich first order logic by allowing quantification over isomorphisms between definable ordered fields the resulting logic, L(Q_{Of}), is fully compact. In this logic, we can give standard compactness proofs of various…
In this paper we study frame definability in finitely-valued modal logics and establish two main results via suitable translations: (1) in finitely-valued modal logics one cannot define more classes of frames than are already definable in…
We give a process for verifying numerical programs against their functional specifications. Our implementation is capable of automatically verifying programs against tight error bounds featuring common elementary functions. We demonstrate…
Verification is one of the central tasks in circuit and system design. While simulation and emulation are widely used, complete correctness can only be ensured based on formal proof techniques. But these approaches often have very high run…
In a recent paper, Belle and Levesque proposed a framework for a type of program called belief programs, a probabilistic extension of GOLOG programs where every action and sensing result could be noisy and every test condition refers to the…
We present a fixpoint semantics of event systems. The semantics is presented in a general framework without concerns of fairness. Soundness and completeness of rules for deriving "leads-to" properties are proved in this general framework.…
In Inverse subsumption for complete explanatory induction Yamamoto et al. investigate which inductive logic programming systems can learn a correct hypothesis $H$ by using the inverse subsumption instead of inverse entailment. We prove that…
This paper presents a proof system for reasoning about execution time bounds for a core imperative programming language. Proof systems are defined for three different scenarios: approximations of the worst-case execution time, exact time…
Axioms are presented which encapsulate the properties satisfied by categories of games which form the basis of results on full abstraction for PCF and other programming languages, and on full completeness for various logics and type…
We present a reinforcement learning (RL) based guidance system for automated theorem proving geared towards Finding Longer Proofs (FLoP). Unlike most learning based approaches, we focus on generalising from very little training data and…
Widely used complex code refactoring tools lack a solid reasoning about the correctness of the transformations they implement, whilst interest in proven correct refactoring is ever increasing as only formal verification can provide true…
Here several perfect simulation algorithms are brought under a single framework, and shown to derive from the same probabilistic result, called here the Fundamental Theorem of Perfect Simulation (FTPS). An exact simulation algorithm has…
We consider logic-based argumentation in which an argument is a pair (Fi,al), where the support Fi is a minimal consistent set of formulae taken from a given knowledge base (usually denoted by De) that entails the claim al (a formula). We…
The logic FO(ID) uses ideas from the field of logic programming to extend first order logic with non-monotone inductive definitions. Such logic formally extends logic programming, abductive logic programming and datalog, and thus formalizes…
Several formal systems, such as resolution and minimal model semantics, provide a framework for logic programming. In this paper, we will survey the use of structural proof theory as an alternative foundation. Researchers have been using…
We present an environment, benchmark, and deep learning driven automated theorem prover for higher-order logic. Higher-order interactive theorem provers enable the formalization of arbitrary mathematical theories and thereby present an…
For each $n\in\mathbb{N}$, let $[n]\phi$ mean "the sentence $\phi$ is true in all $\Sigma_{n+1}$-correct transitive sets." Assuming G\"odel's axiom $V = L$, we prove the following graded variant of Solovay's completeness theorem: the set of…
We consider the explicit fragment of the basic justification stit logic introduced in earlier publications. We define a Hilbert-style axiomatic system for this logic and show that this system is strongly complete relative to the intended…
The continuous modal mu-calculus is a fragment of the modal mu-calculus, where the application of fixpoint operators is restricted to formulas whose functional interpretation is Scott-continuous, rather than merely monotone. By…
While most approaches in formal methods address system correctness, ensuring robustness has remained a challenge. In this paper we present and study the logic rLTL which provides a means to formally reason about both correctness and…