Related papers: NP-Logic Systems and Model-Equivalence Reductions
Despite the increasing effectiveness of language models, their reasoning capabilities remain underdeveloped. In particular, causal reasoning through counterfactual question answering is lacking. This work aims to bridge this gap. We first…
We convert, within polynomial-time and sequential processing, an NP-Complete Problem into a real-variable problem of minimizing a sum of Rational Linear Functions constrained by an Asymptotic-Linear-Program. The coefficients and constants…
We systematically investigate the complexity of model checking the existential positive fragment of first-order logic. In particular, for a set of existential positive sentences, we consider model checking where the sentence is restricted…
Stephen Cook posited SAT is NP-Complete in 1971. If SAT is NP-Complete then, as is generally accepted, any polynomial solution of it must also present a polynomial solution of all NP decision problems. It is here argued, however, that NP is…
Model-checking resource logics with production and consumption of resources is a computationally hard and often undecidable problem. We introduce a simple and realistic assumption that there is at least one diminishing resource, that is, a…
An exhaustive survey of categorical propositions is proposed in the present paper, both with respect to their nature and the logical problems raised by them. Through a comparative analysis of Term Logic and First-Order Logic, it is shown…
When applying machine learning to problems in NLP, there are many choices to make about how to represent input texts. These choices can have a big effect on performance, but they are often uninteresting to researchers or practitioners who…
This paper presents the first study of the complexity of the optimization problem for integer linear-exponential programs which extend classical integer linear programs with the exponential function $x \mapsto 2^x$ and the remainder…
Conditional independence reasoning has been shown to be helpful in the context of Bayesian nets to optimize probabilistic inference, and related techniques have been applied to speed up a number of logical reasoning tasks in boolean logic…
This paper relates the well-known Linear Temporal Logic with the logic of propositional schemata introduced by the authors. We prove that LTL is equivalent to a class of schemata in the sense that polynomial-time reductions exist from one…
This paper focuses on the expressive power of disjunctive and normal logic programs under the stable model semantics over finite, infinite, or arbitrary structures. A translation from disjunctive logic programs into normal logic programs is…
The infinitary propositional logic of here-and-there is important for the theory of answer set programming in view of its relation to strongly equivalent transformations of logic programs. We know a formal system axiomatizing this logic…
Proof equivalence in a logic is the problem of deciding whether two proofs are equivalent modulo a set of permutation of rules that reflects the commutative conversions of its cut-elimination procedure. As such, it is related to the…
As well known, weak K4 and the difference logic DL do not enjoy the Craig interpolation property. Our concern here is the problem of deciding whether any given implication does have an interpolant in these logics. We show that the…
Propositional and modal inclusion logic are formalisms that belong to the family of logics based on team semantics. This article investigates the model checking and validity problems of these logics. We identify complexity bounds for both…
It is proved in this paper that to every underdetermined linear system $Ax=b$ there corresponds a constant $p(A,b)>0$ such that every solution to the $l_p$-norm minimization problem also solves the $l_0$-norm minimization problem whenever…
Optimization is a key task in a number of applications. When the set of feasible solutions under consideration is of combinatorial nature and described in an implicit way as a set of constraints, optimization is typically NP-hard.…
Probabilistic model checking for stochastic games enables formal verification of systems that comprise competing or collaborating entities operating in a stochastic environment. Despite good progress in the area, existing approaches focus…
In this paper, we initiate a systematic study of the parametrised complexity in the field of Dependence Logics which finds its origin in the Dependence Logic of V\"a\"an\"anen from 2007. We study a propositional variant of this logic (PDL)…
The paper proposes a logical model of combinatorial problems, also it gives an example of a problem of the class NP that can not be solved in polynomial time on the dimension of the problem.