Duality between Unprovability and Provability in Forward Refutation-search for Intuitionistic Propositional Logic

The inverse method is a saturation-based theorem-proving technique; it relies on a forward proof-search strategy and can be applied to cut-free calculi enjoying the subformula property. Here, we apply this method to derive the unprovability of a goal formula G in Intuitionistic Propositional Logic. To this aim we design a forward calculus FRJ(G) for Intuitionistic unprovability, which is appropriate for constructively ascertaining the unprovability of a formula G by providing a concise countermodel for it; in particular, we prove that the generated countermodels have minimal height. Moreover, we clarify the role of the saturated database obtained as result of a failed proof-search in FRJ(G) by showing how to extract from such a database a derivation witnessing the Intuitionistic validity of the goal

Answer Set Semantics vs. Information Term Semantics

Abstract We compare Answer Set semantics for propositional theories and Fcl, a constructive logic introduced in [8].

Proof-Search in Natural Deduction Calculus for Classical Propositional Logic

We address the problem of proof-search in the natural deduction calculus for Classical propositional logic. Our aim is to improve the usual na\uefve proof-search procedure where introduction rules are applied upwards and elimination rules downwards. In particular, we introduce NCR, a variant of the usual natural deduction calculus for Classical propositional logic, and we show that it can be used as a base for a proof-search procedure which does not require backtracking nor loop-checking

JTabWb: a Java Framework for Implementing Terminating Sequent and Tableau Calculi

JTabWb is a Java framework for developing provers based on sequent or tableau calculi. It provides a generic engine which searches for proof of a given goal driven by a user-defined prover. The user is required to define the components of a prover by implementing suitable Java interfaces. In this paper we describe the structure of the framework and the role of its components through a running example. To show the generality of the framework we review some of the provers implemented in JTabWb. Finally, to corroborate the fact that the framework can be used to generate efficient provers, we compare the performances of one of the implemented provers with the state-of-the-art provers for Intuitionistic Propositional Logic

Extracting information from intermediate T-systems

In this paper we will study the problem of uniformly extracting information from constructive and semiconstructive calculi. We will define an information extraction mechanism and we will explain several examples of systems to which such a mechanism can be applied. In particular, we will give as examples some families of effective subsystems of a wide class of very large intermediate theories, we call T-systems. These large T-systems, even if ineffective and semantically defined, provide a uniform and fruitful framework where to analyze the possible combinations in a uniformly constructive context of mathematical and super-intuitionistic logical principles. 1 Introduction It is well known that formal proofs can be used for program synthesis and program verification, and this essentially depends on the availability of an information extraction mechanism allowing to capture in an uniform way the implicit algorithmic content of a proof. As is well known (see, e.g., [11, 14]), such a unifo..