1,721,141 research outputs found
Conditional Objects as Possibilistic Variables
No full textSymbolic and Quantitative Approaches to Reasoning with Uncertainty.- 17th European Conference, ECSQARU 2023, Arras, France, September 19–22, 2023, Proceedings.- Conference proceedings.- Published 19 November 2023The interpretation of basic conditionals as three-valued objects initiated by de Finetti has been mainly developed and extended by Gilio and Sanfilippo and colleagues, who look at (compound) conditionals as probabilistic random quantities. Recently, it has been shown that this approach ends up providing a Boolean algebraic structure for the set of conditional objects. In this paper, we show how that this probabilistic-based approach can also be developed within the possibilistic framework, where conditionals are attached with possibilistic variables instead: variables attached with a (conditional) possibility distribution on its domain of plain events. The possibilistic expectation of these variables now provides a means of extending the original possibility distribution on events to (compound) conditional objects. Our main result shows that this possibilistic approach leads to exactly the same underlying Boolean algebraic structure for the set of conditionals.The authors also acknowledge support by the support by the MOSAIC project (EU H2020-MSCA-RISE-2020 Project 101007627) and by the Spanish projects PID2019-111544GB-C21 and PID2022-139835NB-C21 funded by MCIN/AEI/10.13039/501100011033.Peer reviewe
An approach to improve argumentation-based epistemic planning with contextual preferences
No full textCurrent approaches to argumentation-based planning represent an interesting proposal where defeasible argumentation is used as a practical mechanism suitable for reasoning with potentially contradictory information in dynamic environments. In many real-world planning scenarios, the development of formalisms allowing explicit preference specification over pieces of knowledge turns out to be an essential task—however, despite its importance, existing planning systems are not provided with the possibility of dynamically changing these preferences when a plan is being constructed. This paper presents an argumentation-based approach to deal with the handling of preferences when a plan is formulated; in particular, we propose using conditional expressions to select and change priorities regarding information upon which plans are constructed. Our aim is not to improve the efficiency of current planning systems, but to enhance the resulting plan itself by introducing an approach capable of representing and handling multiple preferences over defeasible knowledge. This approach will contribute to the strengthening of existing argumentation-based epistemic planning systems, providing a useful tool that the user could exploit. Finally, we also present a running-time analysis and several complexity results associated with our approach
Expanding FL e w with a Boolean connective
No full textWe expand FL e w with a unary connective whose algebraic counterpart is the operation that gives the greatest complemented element below a given argument. We prove that the expanded logic is conservative and has the Finite Model Property. We also prove that the corresponding expansion of the class of residuated lattices is an equational class. © 2016, Springer-Verlag Berlin Heidelberg.The authors are thankful to annonymous reviewer for his/her comments that have helped to improve the final layout of this paper. The authors have been funded by the EU H2020-MSCA-RISE-2015 Project 689176–SYSMICS. Esteva and Godo have been also funded by the FEDER/MINECO Spanish project TIN2015-71799-C2-1-PPeer Reviewe
Corrigendum to “Towards a probability theory for product logic: States, integral representation and reasoning” [Int. J. Approx. Reason. 93 (2018) 199–218]
No full textThe aim of this short note is to report on a counter-example by Stefano Aguzzoli (private communication) showing that a claim made in a recent paper of ours [2, Proposition 5.2], stating that the class of states of a free product algebra is closed, is in fact not true. That claim was used in turn in the proof of one of the main results of the same paper [2, Theorem 5.4]. However, we also provide in this note an alternative proof for that result, so that it keeps holding true.The authors acknowledge partial support by the SYSMICS project (EU H2020-MSCA-RISE-2015 Project 689176). Also, Flaminio acknowledges partial support by the Spanish Ramon y Cajal research program RYC-2016-19799; Flaminio and Godo acknowledge partial support by the FEDER/MINECO project TIN2015-71799-C2-1-P.Peer reviewe
Finite Satisfiability in Infinite-Valued Lukasiewicz Logic
No full textAlthough it is well-known that every satisfiable formula in Lukasiewicz' infinite-valued logic L-infinity can be satisfied in some finite-valued logic, practical methods for finding an appropriate number of truth degrees do currently not exist. As a first step towards efficient reasoning in L-infinity, we propose a method to find a tight upper bound on this number which, in practice, often significantly improves the worst-case tipper bound of Aguzzoli et al
Similarity-Based Logics for Approximate Entailments. Quantitative Logic and Soft Computing
No full textReasoning under practical circumstances is often inexact. Assumptions
might be fulfilled only in an approximate way but conclusions are drawn anyway.
Different epistemic aspects may be involved, like uncertainty, preference or similarity. In order to formalise such kind of reasoning we need to go beyond classical
propositional logic. In this presentation we will deal with logics for similarity-based
reasoning. This kind of reasoning can be cast in the more general framework of reasoning by analogy and has applications, for example, in classification, case-based
reasoning, or interpolation.The author acknowledges partial support by the Spanish MINECO/FEDER
project RASO (TIN2015-71799-C2-1-P)Peer reviewe
On Product Logic with Truth-constants
Full text linkProduct Logic Π is an axiomatic extension of Hájek's Basic Fuzzy Logic BL coping with the 1-tautologies when the strong conjunction & and implication → are interpreted by the product of reals in [0, 1] and its residuum respectively. In this paper we investigate expansions of Product Logic by adding into the language a countable set of truth-constants (one truth-constant r\#304; for each r in a countable Π-subalgebra of [0, 1]) and by adding the corresponding book-keeping axioms for the truthconstants. We first show that the corresponding logics Π() are algebraizable, and hence complete with respect to the variety of Π()-algebras. The main result of the paper is the canonical standard completeness of these logics, that is, theorems of Π() are exactly the 1-tautologies of the algebra defined over the real unit interval where the truth-constants are interpreted as their own values. It is also shown that they do not enjoy the canonical strong standard completeness, but they enjoy it for finite theories when restricted to evaluated Π-formulas of the kind r\#304; → φ, where r\#304; is a truth-constant and φ a formula not containing truth-constants. Finally we consider the logics ΠΔ(), the expansion of Π() with the well-known Baaz's projection connective Δ, and we show canonical finite strong standard completeness for them.Fil: Savický, Petr. Academy of Sciences of the Czech Republic; República ChecaFil: Cignoli, Roberto Leonardo Oscar. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; ArgentinaFil: Esteva, Francesc. Institut d’Investigacio en Intelligencia Artificial; EspañaFil: Godo, Lluis. Institut d’Investigacio en Intelligencia Artificial; EspañaFil: Nogura, Carles. Institut d’Investigacio en Intelligencia Artificial; Españ
An elementary belief function logic
No full textNon-additive uncertainty theories, typically possibility theory, belief functions and imprecise probabilities share a common feature with modal logic: the duality properties between possibility and necessity measures, belief and plausibility functions as well as between upper and lower probabilities extend the duality between possibility and necessity modalities to the graded environment. It has been shown that the all-or-nothing version of possibility theory can be exactly captured by a minimal epistemic logic (MEL) that uses a very small fragment of the KD modal logic, without resorting to relational semantics. Independently, a belief function logic has been obtained by extending the modal logic S5 to probabilistic graded modalities using Łukasiewicz logic, albeit using relational semantics. This paper shows that a simpler belief function logic can be devised by adding Łukasiewicz logic on top of MEL. It allows for a more natural semantics in terms of Shafer basic probability assignments.Godo acknowledges partial support by Europea Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 101007627 and by the Agencia Estatal de Investigación AEI/10.13039/501100011033 under the grant PID2019-111544GB-C21.Peer reviewe
On Nilpotent Minimum logics defined by lattice filters and their paraconsistent non-falsity preserving companions
No full textNilpotent Minimum logic (NML) is a substructural algebraizable logic that is a distinguished member of the family of systems of Mathematical Fuzzy logic, and at the same time it is the axiomatic extension with the prelinearity axiom of Nelson and Markov’s Constructive logic with strong negation. In this paper our main aim is to characterize and axiomatize paraconsistent variants of NML and its extensions defined by (sets of) logical matrices over linearly ordered NM-algebra with lattice filters as designated values, with special emphasis on those that only exclude the falsum truth-value, called non-falsity preserving logics. We also consider turning these non-falsity preserving logics into Logics of Formal Inconsistency by expanding them with a consistency operator, and we axiomatize them as well. Finally, we provide a full description of the logics defined by finite products of matrices over finite NM-chains.The authors thank the anonymous reviewers for their helpful comments that have significantly helped to improve the layout of this paper. The authors acknowledge support by the MOSAIC project (EU H2020-MSCA-RISE Project 101007627). Gispert acknowledges partial support by the Spanish project SHORE (PID2022-141529NB-C21), while Esteva and Godo by the Spanish project LINEXSYS (PID2022-139835NB-C21), both funded by MCIU/AEI/10.13039/501100011033. Gispert also acknowledges the project 2021 SGR 00348 funded by AGAUR. Coniglio acknowledges support from the National Council for Scientific and Technological Development (CNPq, Brazil) through the individual research grant # 309830/2023-0, and from the São Paulo Research Foundation (FAPESP, Brazil) trough the Thematic Project Rationality, logic and probability—RatioLog, grant #2020/16353-3.Peer reviewe
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