Symmetric blocking

Areces, Carlos; Orbe, Ezequiel

doi:10.1016/j.tcs.2015.06.020

Cited by 2 publications

(1 citation statement)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The use of blocking conditions to stop further application of inference rules while retaining completeness is routinely exploited in automated reasoning, especially in the context of modal (Bolander and Blackburn 2007;Schmidt and Waldmann 2015;Areces and Orbe 2015), temporal (Reynolds 2016;Chafik et al 2021), and description logics (Horrocks and Sattler 1999;Schmidt and Tishkovsky 2011;Glimm, Horrocks, and Motik 2010).…”

Section: Related Workmentioning

confidence: 99%

Materialisation-Based Reasoning in DatalogMTL with Bounded Intervals

Wałęga

Zawidzki

Wang

et al. 2023

AAAI

View full text Add to dashboard Cite

DatalogMTL is a powerful extension of Datalog with operators from metric temporal logic (MTL), which has received significant attention in recent years. In this paper, we investigate materialisation-based reasoning (a.k.a. forward chaining) in the context of DatalogMTL programs and datasets with bounded intervals, where partial representations of the canonical model are obtained through successive rounds of rule applications. Although materialisation does not naturally terminate in this setting, it is known that the structure of canonical models is ultimately periodic. Our first contribution in this paper is a detailed analysis of the periodic structure of canonical models; in particular, we formulate saturation conditions whose satisfaction by a partial materialisation implies an ability to recover the full canonical model via unfolding; this allows us to compute the actual periods describing the repeating parts of the canonical model as well as to establish concrete bounds on the number of rounds of rule applications required to achieve saturation. Based on these theoretical results, we propose a practical reasoning algorithm where saturation can be efficiently detected as materialisation progresses, and where the relevant periods used to evaluate entailment of queries via unfolding are efficiently computed. We have implemented our algorithm and our experiments suggest that our approach is both scalable and robust.

show abstract

Section: Related Workmentioning

confidence: 99%

Materialisation-Based Reasoning in DatalogMTL with Bounded Intervals

Wałęga

Zawidzki

Wang

et al. 2023

AAAI

View full text Add to dashboard Cite

show abstract

Symmetries in Modal Logics

Areces¹,

Orbe²

2015

Bull. symb. log

Self Cite

View full text Add to dashboard Cite

In this paper we develop the theoretical foundations to exploit symmetries in modal logics. We generalize the notion of symmetries of propositional formulas in conjunctive normal form to modal formulas using the framework provided by coinductive modal models introduced in [5]. Hence, the results apply to a wide class of modal logics including, for example, hybrid logics. We present two graph constructions that enable the reduction of symmetry detection in modal formulas to the graph automorphism detection problem, and we evaluate the graph constructions on modal benchmarks. §1. Symmetries in Automated Theorem Proving. Symmetry is a familiar notion. Intuitively, we say that an object is symmetric if "under any kind of transformation at least one property of the object is left invariant" [25]. Symmetry has many uses. Not only can we study the symmetric properties of an object (geometric, mathematical, etc.) to understand its behavior, but we can also derive specific consequences regarding the object under study based on its symmetry properties, i.e., using a "symmetry-based argument" [33]. In automated reasoning, many problem classes, in particular those arising from real world applications, present symmetries, and their presence is usually a source of additional complexity since we might end up looking for solutions in symmetrical subspaces of the problem's search space. Ideally, if we can recognize that such symmetries exist, we might use them to direct a search algorithm to look for solutions only in nonsymmetric parts of the search space, thus reducing the overall difficulty [42].In this context, a symmetry can be defined as a permutation of the variables (or literals) of the input formula that preserves its structure and its solutions. Symmetries can be classified into semantic or syntactic [14]. Semantic symmetries are permutations of the formula that preserves its set of the models (or solutions) and, therefore, can be regarded as properties of the underlying Boolean function, independent of the particular syntactic representation. For example, consider the Boolean function f(a, b, x, y) = axy + bxy, where a, b, x, y take values over {0, 1} and sum and product are binary. It is straightforward to verify that the permutation that interchanges the parameters a and b leaves the function unchanged, maintaining its set of solutions. Syntactic symmetries, on the other hand, correspond to the

show abstract

Symmetric blocking

Cited by 2 publications

References 12 publications

Materialisation-Based Reasoning in DatalogMTL with Bounded Intervals

Materialisation-Based Reasoning in DatalogMTL with Bounded Intervals

Symmetries in Modal Logics

Contact Info

Product

Resources

About