Related papers: Tableau Proof Systems for Justification Logics
We present a method to prove the decidability of provability in several well-known inference systems. This method generalizes both cut-elimination and the construction of an automaton recognizing the provable propositions.
We present a system for the investigation of computational properties of categorial grammar parsing based on a labelled analytic tableaux theorem prover. This proof method allows us to take a modular approach, in which the basic grammar can…
Models of complex systems are widely used in the physical and social sciences, and the concept of layering, typically building upon graph-theoretic structure, is a common feature. We describe an intuitionistic substructural logic called…
We give an optimal (EXPTIME), sound and complete tableau-based algorithm for deciding satisfiability for propositional dynamic logic with converse (CPDL) which does not require the use of analytic cut. Our main contribution is a sound…
In this paper we present a proof system that operates on graphs instead of formulas. Starting from the well-known relationship between formulas and cographs, we drop the cograph-conditions and look at arbitrary undirected) graphs. This…
In this paper we compare two proof systems for minimal entailment: a tableau system OTAB and a sequent calculus MLK, both developed by Olivetti (1992). Our main result shows that OTAB-proofs can be efficiently translated into MLK-proofs,…
These lecture notes survey the emerging area of Universal Proof Theory, which investigates general questions about the existence, equivalence, and characterization of good proof systems for broad classes of logics. In particular, the notes…
In this note, by integrating ideas concerning terminating tableaux-based procedures in modal logics and finite frame property of intuitionistic modal logic IK, we provide new and simpler decidability proofs for FIK and LIK.
We present a syntactic cut-elimination procedure for the alternation-free fragment of the modal mu-calculus. Cut reduction is carried out within a cyclic proof system, where proofs are finitely branching but may be non-wellfounded. The…
We present a game semantics for Linear Logic, in which formulas denote games and proofs denote winning strategies. We show that our semantics yields a categorical model of Linear Logic and prove full completeness for Multiplicative Linear…
By a pure logical framework we mean a framework which does not rely on any particular formal calculus. For example, Metamath is an instance of a pure logical framework. Another example is the Russell system…
We offer the proofs that complete our article introducing the propositional calculus called semi-intuitionistic logic with strong negation.
In this paper, we investigate the proof complexity of a wide range of substructural systems. For any proof system $\mathbf{P}$ at least as strong as Full Lambek calculus, $\mathbf{FL}$, and polynomially simulated by the extended Frege…
There are many techniques and tools to prove termination of C programs, but up to now these tools were not very powerful for fully automated termination proofs of programs whose termination depends on recursive data structures like lists.…
A many-valued modal logic is introduced that combines the usual Kripke frame semantics of the modal logic K with connectives interpreted locally at worlds by lattice and group operations over the real numbers. A labelled tableau system is…
The features of a logically sound approach to a theory of statistical reasoning are discussed. A particular approach that satisfies these criteria is reviewed. This is seen to involve selection of a model, model checking, elicitation of a…
In prior work, we showed that logic programming compilation can be given a proof-theoretic justification for generic abstract logic programming languages, and demonstrated this technique in the case of hereditary Harrop formulas and their…
Justification theory is a unifying semantic framework. While it has its roots in non-monotonic logics, it can be applied to various areas in computer science, especially in explainable reasoning; its most central concept is a justification:…
The formal analysis of automated systems is an important and growing industry. This activity routinely requires new verification frameworks to be developed to tackle new programming features, or new considerations (bugs of interest). Often,…
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…