Related papers: Translating Three-Variable First-Order Predicate L…
This article describes an evaluation of Automated Theorem Proving (ATP) systems on problems taken from the QMLTP library of first-order modal logic problems. Principally, the problems are translated to both typed first-order and…
We describe here a simple application of rational trees to the implementation of an interpreter for a procedural language written in a logic programming language. This is possible in languages designed to support rational trees (such as…
Program logics are a powerful formal method in the context of program verification. Can we develop a counterpart of program logics in the context of language verification? This paper proposes language logics, which allow for statements of…
Mechanical proofs by logical relations often involve tedious reasoning about substitution. In this paper, we show that this is not necessarily the case, by developing, in Agda, a proof that all simply typed lambda calculus expressions…
This paper describes a procedure that system developers can follow to translate typical mathematical representations of linearized control systems into logic theories. These theories are then used to verify system requirements and find…
The First-Order Variable Elimination (FOVE) algorithm allows exact inference to be applied directly to probabilistic relational models, and has proven to be vastly superior to the application of standard inference methods on a grounded…
Predicate Logic with Definitions (PLD or D-logic) is a modification of first-order logic intended mostly for practical formalization of mathematics. The main syntactic constructs of D-logic are terms, formulas and definitions. A definition…
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,…
Relational verification is a technique that aims at proving properties that relate two different program fragments, or two different program runs. It has been shown that constrained Horn clauses (CHCs) can effectively be used for relational…
Lin and Zhaos theorem on loop formulas states that in the propositional case the stable model semantics of a logic program can be completely characterized by propositional loop formulas, but this result does not fully carry over to the…
Human ability at solving complex tasks is helped by priors on object and event semantics of their environment. This paper investigates the use of similar prior knowledge for transfer learning in Reinforcement Learning agents. In particular,…
Different theorem provers tend to produce proof objects in different formats and this is especially the case for modal logics, where several deductive formalisms (and provers based on them) have been presented. This work falls within the…
A number of SAT-based analysis concepts and tools for software product lines exist, that extract code dependencies in propositional logic from the source code assets of the product line. On these extracted conditions, SAT-solvers are used…
Higher-order constructs extend the expressiveness of first-order (Constraint) Logic Programming ((C)LP) both syntactically and semantically. At the same time assertions have been in use for some time in (C)LP systems helping programmers…
Automated reasoners, such as SAT/SMT solvers and first-order provers, are becoming the backbones of rigorous systems engineering, being used for example in applications of system verification, program synthesis, and cybersecurity.…
This paper introduces Scavenger, the first theorem prover for pure first-order logic without equality based on the new conflict resolution calculus. Conflict resolution has a restricted resolution inference rule that resembles (a…
In this article the algorithm for transformation of logic functions which are given by truth tables is considered. The suggested algorithm allows the transformation of many-valued logic functions with the required number of variables and…
First-order logic is typically presented as the study of deduction in a setting with elementary quantification. In this paper, we take another vantage point and conceptualize first-order logic as a linear space that encodes "plausibility".…
We show that the decidability of the first-order theory of the language that combines Boolean algebras of sets of uninterpreted elements with Presburger arithmetic operations. We thereby disprove a recent conjecture that this theory is…
We present a formalization of higher-order logic in the Isabelle proof assistant, building directly on the foundational framework Isabelle/Pure and developed to be as small and readable as possible. It should therefore serve as a good…