CSL-lean: A Theorem-prover for the Logic of Comparative Concept Similarity

Alenda, Régis; Olivetti, Nicola; Pozzato, Gian Luca

doi:10.1016/j.entcs.2010.04.002

Cited by 6 publications

(6 citation statements)

References 15 publications

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“…By (A21), there is an i such that ε i ∧ ♦ ϕ ≈ ⊥. In particular, W is the set of atoms of L. We conclude that the mapping e : B → P(W ) defined by (2), that is,…”

Section: Approximate Entailment On Products Of Chainsmentioning

confidence: 76%

“…We call the former variables sorted and the latter unsorted. 2 Basic expressions of LAEPC as well as graded implications and formulas are defined as in case of LAEC. We will keep using B to denote the set of basic expressions of LAEPC.…”

Section: Approximate Entailment On Products Of Chainsmentioning

confidence: 99%

“…Logics for spaces endowed with a metric or a more general distance function have been considered in a series of contributions by Kutz et al, see, e.g., [16,17]. Furthermore, logics on comparative similarity have been studied by Alenda et al, see, e.g., [1,2,3]. It is also worth mentioning that there are some connections with graded or fuzzy consequence relations as studied by Pavelka [21,20], Chakraborty [6,7], and Gerla [12] among others in the context of many-valued logics, since indeed, graded implications α > c β capture, at a syntactic (meta-)level, the idea of β being a consequence of α to the degree c. However, in the present context, α and β are classical propositions, not many-valued ones.…”

Section: Introductionmentioning

confidence: 99%

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Logics for Approximate Entailment in ordered universes of discourse

Vetterlein

Esteva

Godo

2016

International Journal of Approximate Reasoning

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The Logic of Approximate Entailment (LAE) is a graded counterpart of classical propositional calculus, where conclusions that are only approximately correct can be drawn. This is achieved by equipping the underlying set of possible worlds with a similarity relation. When using this logic in applications, however, a disadvantage must be accepted; namely, in LAE it is not possible to combine conclusions in a conjunctive way. In order to overcome this drawback, we propose in this paper a modification of LAE where, at the semantic level, the underlying set of worlds is moreover endowed with an order structure. The chosen framework is designed in view of possible applications. *

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“…By (A21), there is an i such that ε i ∧ ♦ ϕ ≈ ⊥. In particular, W is the set of atoms of L. We conclude that the mapping e : B → P(W ) defined by (2), that is,…”

Section: Approximate Entailment On Products Of Chainsmentioning

confidence: 76%

Section: Approximate Entailment On Products Of Chainsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Logics for Approximate Entailment in ordered universes of discourse

Vetterlein

Esteva

Godo

2016

International Journal of Approximate Reasoning

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“…The program comprises a set of clauses, each one of them implementing a sequent rule or an axiom of LSE and its extensions. The proof search is provided for free by the mere depthfirst search mechanism of Prolog, without any additional ad hoc mechanism, following the line of the theorem provers for modal and conditional logics in [1,8,15,16,17,18,19] and for preferential reasoning [6] in [7]. In the case of EM we consider both the modular version like in Fig.…”

Section: Design Of Pronommentioning

confidence: 99%

“…In this paper we describe PRONOM (theorem PROver for NOnnormal Modal logics) a Prolog theorem prover for the classical cube of non-normal modal logics 1 . The prover PRONOM implements the labelled sequent calculi presented in [5].…”

Section: Introductionmentioning

confidence: 99%

Proof-search and countermodel generation for non-normal modal logics: The theorem prover PRONOM

Dalmonte

Negri

Olivetti

et al. 2021

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In this work we present PRONOM, a theorem prover and countermodel generator for non-normal modal logics. PRONOM implements some labelled sequent calculi recently introduced for the basic system E and its extensions with axioms M, N, and C based on bi-neighbourhood semantics. PRONOM is inspired by the methodology of leanTAP and is implemented in Prolog. When a modal formula is valid, then PRONOM computes a proof (a closed tree) in the labelled calculi having a sequent with an empty left-hand side and containing only that formula on the right-hand side as a root, otherwise PRONOM is able to extract a model falsifying it from an open, saturated branch. The paper shows some experimental results, witnessing that the performances of PRONOM are promising.

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