Related papers: CERES in Propositional Proof Schemata
Urban and Bierman introduced a calculus of proof terms for the sequent calculus LK with a strongly normalizing reduction relation. We extend this calculus to simply-typed higher-order logic with inferences for induction and equality, albeit…
We present a novel decision tree-based synthesis algorithm of ranking functions for verifying program termination. Our algorithm is integrated into the workflow of CounterExample Guided Inductive Synthesis (CEGIS). CEGIS is an iterative…
The key to the proof-theoretic study of a logic is a proof calculus with a subformula property. Many different proof formalisms have been introduced (e.g. sequent, nested sequent, labelled sequent formalisms) in order to provide such…
One of the key concepts in testing is that of adequate test sets. A test selection criterion decides which test sets are adequate. In this paper, a language schema for specifying a large class of test selection criteria is developed; the…
Chase algorithms are indispensable in the domain of knowledge base querying, which enable the extraction of implicit knowledge from a given database via applications of rules from a given ontology. Such algorithms have proved beneficial in…
Representing a proof tree by a combinator term that reduces to the tree lets subtle forms of duplication within the tree materialize as duplicated subterms of the combinator term. In a DAG representation of the combinator term these…
We design a proof system for propositional classical logic that integrates two languages for Boolean functions: standard conjunction-disjunction-negation and binary decision trees. We give two reasons to do so. The first is…
Top-down induction of decision trees has been observed to suffer from the inadequate functioning of the pruning phase. In particular, it is known that the size of the resulting tree grows linearly with the sample size, even though the…
One of the long-standing problems on logic programming is to express {\it priority}-related operations -- default reasoning, if-then-else, cut, exception handling, etc -- in a high-level way. We argue that this problem can be solved by…
Basic proof-search tactics in logic and type theory can be seen as the root-first applications of rules in an appropriate sequent calculus, preferably without the redundancies generated by permutation of rules. This paper addresses the…
Motivated by applications in automated verification of higher-order functional programs, we develop a notion of constrained Horn clauses in higher-order logic and a decision problem concerning their satisfiability. We show that, although…
The Sum-of-Squares (SoS) hierarchy, also known as Lasserre hierarchy, has emerged as a promising tool in optimization. However, it remains unclear whether fixed-degree SoS proofs can be automated [O'Donnell (2017)]. Indeed, there are…
Proof terms are syntactic expressions that represent computations in term rewriting. They were introduced by Meseguer and exploited by van Oostrom and de Vrijer to study equivalence of reductions in (left-linear) first-order term rewriting…
Lifting attempts to speed up probabilistic inference by exploiting symmetries in the model. Exact lifted inference methods, like their propositional counterparts, work by recursively decomposing the model and the problem. In the…
Many practical problems are characterized by a preference relation over admissible solutions, where preferred solutions are minimal in some sense. For example, a preferred diagnosis usually comprises a minimal set of reasons that is…
This paper develops an algorithmic-based approach for proving inductive properties of propositional sequent systems such as admissibility, invertibility, cut-elimination, and identity expansion. Although undecidable in general, these…
Elucidating the reasoning process with structured explanations from question to answer is crucial, as it significantly enhances the interpretability, traceability, and trustworthiness of question-answering (QA) systems. However, structured…
Blocked clauses provide the basis for powerful reasoning techniques used in SAT, QBF, and DQBF solving. Their definition, which relies on a simple syntactic criterion, guarantees that they are both redundant and easy to find. In this paper,…
The semantics of the Prolog ``cut'' construct is explored in the context of some desirable properties of logic programming systems, referred to as the witness properties. The witness properties concern the operational consistency of…
A logic is presented for reasoning on iterated sequences of formulae over some given base language. The considered sequences, or "schemata", are defined inductively, on some algebraic structure (for instance the natural numbers, the lists,…