Related papers: Between proof construction and SAT-solving
Possibilistic computation tree Logic (PoCTL) is one kind of branching temporal logic combined with uncertain information in possibility theory, which was introduced in order to cope with the systematic verification on systems with uncertain…
We present algorithms based on satisfiability problem (SAT) solving, as well as answer set programming (ASP), for solving the problem of determining inconsistency degrees in propositional knowledge bases. We consider six different…
Reachability Logic is a formalism that can be used, among others, for expressing partial-correctness properties of transition systems. In this paper we present three proof systems for this formalism, all of which are sound and complete and…
It is well-know that deciding consistency for normal answer set programs (ASP) is NP-complete, thus, as hard as the satisfaction problem for classical propositional logic (SAT). The best algorithms to solve these problems take exponential…
Many natural combinatorial problems can be expressed as constraint satisfaction problems. This class of problems is known to be NP-complete in general, but certain restrictions on the form of the constraints can ensure tractability. The…
Recent results show that a constraint satisfaction problem (CSP) defined over rational numbers with their natural ordering has a solution if and only if it has a definable solution. The proof uses advanced results from topology and modern…
Many logic programming based approaches can be used to describe and solve combinatorial search problems. On the one hand there are definite programs and constraint logic programs that compute a solution as an answer substitution to a query…
The Promise Constraint Satisfaction Problem (PCSP) is a generalization of the Constraint Satisfaction Problem (CSP) that includes approximation variants of satisfiability and graph coloring problems. Barto [LICS '19] has shown that a…
Boolean Satisfiability (SAT) and Satisfiability Modulo Theories (SMT) are widely used in automated verification, but there is a lack of interactive tools designed for educational purposes in this field. To address this gap, we present…
The structure of satisfiability problems is used to improve search algorithms for quantum computers and reduce their required coherence times by using only a single coherent evaluation of problem properties. The structure of random k-SAT…
Answer set programming (ASP) is a logic programming paradigm that can be used to solve complex combinatorial search problems. Aggregates are an ASP construct that plays an important role in many applications. Defining a satisfactory…
We investigate the complexity of the model checking problem for intuitionistic and modal propositional logics over transitive Kripke models. More specific, we consider intuitionistic logic IPC, basic propositional logic BPL, formal…
This work, shows how propositional resolution can be generalized to obtain a resolution proof system for constrained pseudo-propositional logic (CPPL), which is an extension resulted from inserting the natural numbers with few constraints…
The logic of bunched implication BI provides a framework for reasoning about resource composition and forms the basis for an assertion language of separation logic which is used to reason about software programs. Propositional BI is…
The interest in explainability in artificial intelligence (AI) is growing vastly due to the near ubiquitous state of AI in our lives and the increasing complexity of AI systems. Answer-set Programming (ASP) is used in many areas, among them…
Recent authors have proposed analyzing conditional reasoning through a notion of intervention on a simulation program, and have found a sound and complete axiomatization of the logic of conditionals in this setting. Here we extend this…
This paper reviews the recent literature on solving the Boolean satisfiability problem (SAT), an archetypal NP-complete problem, with the help of machine learning techniques. Despite the great success of modern SAT solvers to solve large…
We define a logic of propositional formula schemata adding to the syntax of propositional logic indexed propositions and iterated connectives ranging over intervals parameterized by arithmetic variables. The satisfiability problem is shown…
For each integer $n$ we present an explicit formulation of a compact linear program, with $O(n^3)$ variables and constraints, which determines the satisfiability of any 2SAT formula with $n$ boolean variables by a single linear…
In this paper, we show that the derivability problem for the primal propositional logic remains solvable in polynomial time upon adding a certain form of the principle of equivalent form substitution; and that, upon adding another form of…