Efficient strategies for Automated reasoning in modal logics

Demri, Stéphane

doi:10.1007/bfb0021972

Cited by 3 publications

(3 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For non-classical logics, there are not so many automated reasoning tools and test problems. Here we describe some experimental results on the benchmarks used by other authors [1,3,9,6]. We shall not elaborate on the programs' performances, because they are affected by several factors such as the data structures and the programming languages.…”

Section: Resultsmentioning

confidence: 99%

See 1 more Smart Citation

On the Relational Translation Method for Propositional Modal Logics

Zhang¹

2021

Preprint

View full text Add to dashboard Cite

One way of proving theorems in modal logics is translating them into the predicate calculus and then using conventional resolutionstyle theorem provers. This approach has been regarded as inappropriate in practice, because the resulting formulas are too lengthy and it is impossible to show the non-theoremhood of modal formulas. In this paper, we demonstrate the practical feasibility of the (relational) translation method. Using a state-of-the-art theorem prover for firstorder predicate logic, we proved many benchmark theorems available from the modal logic literature. We show the invalidity of propositional modal and temporal logic formulas, using model generators or satisfiability testers for the classical logic. Many satisfiable formulas are found to have very small models. Finally, several different approaches are compared.

show abstract

Section: Resultsmentioning

confidence: 99%

“…Demri [3] analyses several different strategies in a tableau-based S4 prover, and compares them on a set of 9 valid formulas. Here we list 4 of them:…”

Section: Problem Setmentioning

confidence: 99%

On the Relational Translation Method for Propositional Modal Logics

Zhang¹

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…The common feature of the all these logics is that their models may contain essentially independent sub-models, such that denotations of operators are unions of their denotation in each sub model. 5 3.9 An extended 0-order reasoning algorithm (EZORA) If the operators of L 0 satisfy the property P then consistency of the expressions of L + 0 can be de ned in terms of the entailment relation, j = L0 , of L 0 as follows: hM; Ei is consistent i there is no formula p 2 E such that M j = L0 p Otherwise it is inconsistent, in which case we write hM; Ei j = L + 0 ? This should make clear why the formulae in E are called`entailment constraints'.…”

Section: Ifmentioning

confidence: 99%

Modal Logics for Qualitative Spatial Reasoning

Bennett¹

1996

Logic Jnl IGPL

View full text Add to dashboard Cite

Spatial reasoning is essential for many AI applications. In most existing systems the representation is primarily numerical, so the information that can be handled is limited to precise quantitative data. However, for many purposes the ability to manipulate high-level qualitative spatial information in a exible way would be extremely useful. Such capabilities can be proveded by logical calculi; and indeed 1st-order theories of certain spatial relations have been given 20]. But computing inferences in 1st-order logic is generally intractable unless special (domain dependent) methods are known. 0-order modal logics provide an alternative representation which is more expressive than classical 0-order logic and yet often more amenable to automated deduction than 1st-order formalisms. These calculi are usually interpreted as propositional logics: non-logical constants are taken as denoting propositions. However, they can also be given a nominal interpretation in which the constants stand for some kind of object. I show how 0-order logics can be given a spatial interpretation: constants denote regions and logical operators correspond to operations on regions which are important for characterising spatial situations.Representing certain spatial concepts requires the introduction of modal operators, interpreted as functions generating regions related in speci c ways to those denoted by their arguments. A signi cant example is the convex-hull operator whose value is the smallest convex region containing its argument. I investigate how this this operator can be captured in a multi-modal logic.

show abstract