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Tabled logic programming is receiving increasing attention in the Logic Programming community. It avoids many of the shortcomings of SLD execution and provides a more flexible and often extremely efficient execution mechanism for logic…
We present an incomplete proof synthesis method for the Calculus of Constructions which is always terminating and a complete Vernacular for the Calculus of Constructions based on this method.
Using appropriate notation systems for proofs, cut-reduction can often be rendered feasible on these notations, and explicit bounds can be given. Developing a suitable notation system for Bounded Arithmetic, and applying these bounds, all…
A strong confluence result for Q*, a quantum lambda-calculus with measurements, is proved. More precisely, confluence is shown to hold both for finite and infinite computations. The technique used in the confluence proof is syntactical but…
We consider the quantified constraint satisfaction problem (QCSP) which is to decide, given a structure and a first-order sentence (not assumed here to be in prenex form) built from conjunction and quantification, whether or not the…
Completeness is a desirable property of test suites. Roughly, completeness guarantees that a non-equivalent implementation under test will always be identified. Several approaches proposed sufficient, and sometimes also necessary,…
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…
Boyer and Moore have discussed a recursive function that puts conditional expressions into normal form [1]. It is difficult to prove that this function terminates on all inputs. Three termination proofs are compared: (1) using a measure…
We discuss proving correctness and completeness of definite clause logic programs. We propose a method for proving completeness, while for proving correctness we employ a method which should be well known but is often neglected. Also, we…
The automated generation of exercises may substantially reduce the time educators devote to manual exercise design. A major obstacle to the integration of such automation into teaching practice, however, lies in the ability to control the…
We uncover a close relationship between combinatorial and syntactic proofs for first-order logic (without equality). Whereas syntactic proofs are formalized in a deductive proof system based on inference rules, a combinatorial proof is a…
This paper tackles the problem of formulating and proving the completeness of focused-like proof systems in an automated fashion. Focusing is a discipline on proofs which structures them into phases in order to reduce proof search…
We study the complexity of various fundamental counting problems that arise in the context of incomplete databases, i.e., relational databases that can contain unknown values in the form of labeled nulls. Specifically, we assume that the…
Program synthesis is the task of automatically deriving a program that has been specified by a user in advance. Combining automated theorem proving with program synthesis enables the automated construction of proven-to-be-correct programs,…
The entanglement of formation gives a necessary and sufficient condition for the existence of a perfect quantum error correction procedure.
In various provers and deductive verification tools, logical transformations are used extensively in order to reduce a proof task into a number of simpler tasks. Logical transformations are often part of the trusted base of such tools. In…
Verification proofs encode complete program behavior, yet we discard them after checking correctness. We present compiling by proving, a paradigm that transforms these proofs into optimized execution rules. By constructing All-Path…
We study the complexity of various fundamental counting problems that arise in the context of incomplete databases, i.e., relational databases that can contain unknown values in the form of labeled nulls. Specifically, we assume that the…
The use of logical systems for problem-solving may be as diverse as in proving theorems in mathematics or in figuring out how to meet up with a friend. In either case, the problem solving activity is captured by the search for an…
Several signal recovery tasks can be relaxed into semidefinite programs with rank-one minimizers. A common technique for proving these programs succeed is to construct a dual certificate. Unfortunately, dual certificates may not exist under…