Related papers: Complete Cyclic Proof Systems for Inductive Entail…
A cyclic proof system generalises the standard notion of a proof as a finite tree of locally sound inferences by allowing proof objects to be potentially infinite. Regular infinite proofs can be finitely represented as graphs. To preclude…
Cyclic proof theory breaks tradition by allowing certain infinite proofs: those that can be represented by a finite graph, while satisfying a soundness condition. We reconcile cyclic proofs with traditional finite proofs: we extend abstract…
This paper investigates the admissibility of the substitution rule in cyclic-proof systems. The substitution rule complicates theoretical case analysis and increases computational cost in proof search since every sequent can be a conclusion…
Despite recent advances in automating theorem proving in full first-order theories, inductive reasoning still poses a serious challenge to state-of-the-art theorem provers. The reason for that is that in first-order logic induction requires…
Logics with team semantics provide alternative means for logical characterization of complexity classes. Both dependence and independence logic are known to capture non-deterministic polynomial time, and the frontiers of tractability in…
Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles…
We define a class of Separation Logic formulae, whose entailment problem: given formulae $\phi, \psi_1, \ldots, \psi_n$, is every model of $\phi$ a model of some $\psi_i$? is 2EXPTIME-complete. The formulae in this class are existentially…
Infinitary and cyclic proof systems are proof systems for logical formulas with fixed-point operators or inductive definitions. A cyclic proof system is a restriction of the corresponding infinitary proof system. Hence, these proof systems…
A sound and complete embedding of conditional logics into classical higher-order logic is presented. This embedding enables the application of off-the-shelf higher-order automated theorem provers and model finders for reasoning within and…
An inductive inference system for proving validity of formulas in the initial algebra $T_{\mathcal{E}}$ of an order-sorted equational theory $\mathcal{E}$ is presented. It has 20 inference rules, but only 9 of them require user interaction;…
Formal reasoning about inductively defined relations and structures is widely recognized not only for its mathematical interest but also for its importance in computer science, and has applications in verifying properties of programs and…
We propose a procedure for automated implicit inductive theorem proving for equational specifications made of rewrite rules with conditions and constraints. The constraints are interpreted over constructor terms (representing data values),…
Despite recent advances in automating theorem proving in full first-order theories, inductive reasoning still poses a serious challenge to state-of-the-art theorem provers. The reason for that is that in first-order logic induction requires…
This paper presents an approach to lemma synthesis to support advanced inductive entailment procedures based on separation logic. We first propose a mechanism where lemmas are automatically proven and systematically applied. The lemmas may…
The notion of clause set cycle abstracts a family of methods for automated inductive theorem proving based on the detection of cyclic dependencies between clause sets. By discerning the underlying logical features of clause set cycles, we…
It is well-known that extending the Hilbert axiomatic system for first-order intuitionistic logic with an exclusion operator, that is dual to implication, collapses the domains of models into a constant domain. This makes it an interesting…
In this chapter, we introduce a new dialogical system for first order classical logic which is close to natural language argumentation, and we prove its completeness with respect to usual classical validity. We combine our dialogical system…
Logic rules and inference are fundamental in computer science and have been studied extensively. However, prior semantics of logic languages can have subtle implications and can disagree significantly, on even very simple programs,…
A cyclic proof system gives us another way of representing inductive definitions and efficient proof search. In 2011 Brotherston and Simpson conjectured the equivalence between the provability of the classical cyclic proof system and that…
Circular (or cyclic) proofs have received increasing attention in recent years, and have been proposed as an alternative setting for studying (co)inductive reasoning. In particular, now several type systems based on circular reasoning have…