Related papers: A Proof Synthesis Algorithm for a Mathematical Ver…
We report on a new, simple, modular, and flexible approach for automated generation of illustrations for (readable) synthetic geometry proofs. The underlying proofs are generated using the Larus automated prover for coherent logic, and…
Although reasoning about equations over strings has been extensively studied for several decades, little research has been done for equational reasoning on general clauses over strings. This paper introduces a new superposition calculus…
We present a version of arithmetic in all finite types which allows for a definition of equality at higher types for which all congruence are derivable, for which the soundness of the Dialectica interpretation is provable inside the system…
We present a proof of completeness for the implicational propositional calculus, based on a variant of the Lindenbaum procedure.
We discuss tableaux for the Implicational Propositional Calculus and show how they may be used to establish its completeness.
We present a calculus, called the scheme-calculus, that permits to express natural deduction proofs in various theories. Unlike $\lambda$-calculus, the syntax of this calculus sticks closely to the syntax of proofs, in particular, no names…
We study a well-known technique of using absoluteness for giving choice-free proofs to some statements which are known to be provable with the axiom of choice. The idea is to reduce the problem to an inner model where the axiom of choice…
We give a procedure for counting the number of different proofs of a formula in various sorts of propositional logic. This number is either an integer (that may be 0 if the formula is not provable) or infinite.
We investigate here a new version of the Calculus of Inductive Constructions (CIC) on which the proof assistant Coq is based: the Calculus of Congruent Inductive Constructions, which truly extends CIC by building in arbitrary first-order…
We prove the syntactic soundness of classical tableaux with free variables and on-the-fly Skolemization. Soundness proofs are usually built from semantic arguments, and this is to our knowledge, the first proof that appeals to syntactic…
Deciding termination is a fundamental problem in the analysis of probabilistic imperative programs. We consider the qualitative and quantitative probabilistic termination problems for an imperative programming model with discrete…
We propose a modular method for proving termination of general logic programs (i.e., logic programs with negation). It is based on the notion of acceptable programs, but it allows us to prove termination in a truly modular way. We consider…
Coping with ambiguity has recently received a lot of attention in natural language processing. Most work focuses on the semantic representation of ambiguous expressions. In this paper we complement this work in two ways. First, we provide…
Extended regular expressions with counting and interleaving are widely used in practice. However the related theoretical studies for this kind of expressions currently cannot meet the need of practical work. This paper develops syntax…
We describe a syntactic method for taking proofs which use ultraproducts and translating them into direct, constructive proofs.
We obtain, for the first time, a modular many-valued semantics for combined logics, which is built directly from many-valued semantics for the logics being combined, by means of suitable universal operations over partial non-deterministic…
Adding rewriting to a proof assistant based on the Curry-Howard isomorphism, such as Coq, may greatly improve usability of the tool. Unfortunately adding an arbitrary set of rewrite rules may render the underlying formal system undecidable…
Synthesis is the automatic construction of a system from its specification. In classical synthesis algorithms, it is always assumed that the system is "constructed from scratch" rather than composed from reusable components. This, of…
Provably correct software is one of the key challenges in our softwaredriven society. While formal verification establishes the correctness of a given program, the result of program synthesis is a program which is correct by construction.…
We study possibilities for automated invariant generation in parametric systems. We use (a refinement of) an algorithm for symbol elimination in theory extensions to devise a method for iteratively strengthening certain classes of safety…