Modal tableaux for nonmonotonic reasoning

The tableau-like proof system KEM has been proven to be able to cope with a wide variety of (normal) modal logics. KEM is based on D'Agostino and Mondadori's (1994) classical proof system KE, a combination of tableau and natural deduction inference rules which allows for a restricted ("analytic") Use of the cut rule. The key feature of KEM, besides its being based neither on resolution nor on standard sequent/tableau inference techniques, is that it generates models and checks them using a label scheme to bookkeep "world" paths. This formalism can be extended to handle various system of multimodal logic devised for dealing with nonmonotonic reasoning, by relying in particular on Meyer and van der Hoek's (1992) logic for actuality and preference. In this paper we shall be concerned with developing a similar extension this time by relying on Schwind and Siegel's (1993,1994) system H, another multimodal logic devised for dealing with nonmonotonic inference

Betting and Presuming: From God’s Existence to Morality and Law

Pascal famously argued that since God transcends the rational domain of demonstration, we must bet on his existence. Less famously, Leibniz claimed that in the absence of a full-fledged demonstration of God’s existence, we at least have to presume, that is to say, to assume, that he exists until the contrary is proved. Aside from marking a significant contrast between these two leading figures of modern philosophy (Leibniz would later reproach Pascal for having “paid attention only to moral arguments”), these two stances are at the origin of two independent developments: decision theory and presumptive reasoning, respectively. In this paper we will provide a critical account of Pascal’s and Leibniz’s lines of thought by first presenting the original arguments and then reconstructing them in light of the developments they gave rise to. Finally, we will advance some remarks about the interplay of presumption and probability in Leibniz’s approach to morality and law

Labelled tableaux for nonmonotonic reasoning: Cumulative consequence relations

In this paper we present a labelled proof method for computing nonmonotonic consequence relations in a conditional logic setting. The method exploits the strong connection between these deductive relations and conditional logics, and it is based on the usual possible world semantics devised for the latter. The label formalism KEM, introduced to account for the semantics of normal modal logics, is easily adapted to the semantics of conditional logic by simply indexing labels with formulas. The basic inference rules are provided by the propositional system KE+ - a tableau-like analytic proof system devised to be used both as a refutation method and a direct method of proof - that is the classical core of KEM which is thus enlarged with suitable elimination rules for the conditional connective. The resulting algorithmic framework is able to compute cumulative consequence relations in so far as they can be expressed as conditional implications

Ensaio sobre novas questões filosóficas extraídas do direito

Este artigo é uma homenagem a Leibniz e a sua obra da juventude Specimen quaestionum philosophicarum ex iure collectarum ("Ensaio de questões filosóficas extraídas do direito"). Neste texto, Leibniz, no início de sua carreira como filósofo e como jurista apresenta a sua (para a época e provavelmente ainda hoje) tese audaciosa de que o direito se oferece espontaneamente à filosofia seja pelo que há nele de intrinsecamente filosófico, seja porque "muitíssimos lugares do direito, sem a condução desta, seriam um labirinto inextricável". No rastro destas teses leibnizianas, o artigo se concentra em três normas do ordenamento jurídico italiano: o art. 1189 do Código Civil italiano (pagamento ao credor aparente); o art. 47 del Código Penal italiano (erro de fato), e o art. 533 do Código de Processo Penal italiano (dúvida razoável). De cada um desses artigos é analisado o alcance filosófico implícito.O primeiro artigo nos leva diretamente ao problema da dicotomia entre realidade e aparência; o segundo põe o problema da nossa representação da realidade, enquanto o terceiro levanta questões acerca da diferença entre dúvida possível e dúvida razoável. Em todos os três casos são também sugeridas algumas possíveis implicações jurisprudenciais da relativa leitura filosófica

KED: a deontic theorem prover

Deontic logic (DL) is increasingly recognized as an indispensable tool in such application areas as formal representation of legal knowledge and reasoning, formal specification of computer systems and formal analysis of database integrity constraints. Despite this acknowledgement, there have been few attempts to provide computationally tractable inference mechanisms for DL. In this paper we shall be concerned with providing a computationally oriented proof method for standard DL (SDL), i.e., normal systems of modal logic with the usual possible-worlds semantics. Because of the natural and easily implementable style of proof construction it uses, this method seems particularly well-suited for applications in the AI and Law field, and though in the present version it works for SDL only, it forms an appropriate basis for developing efficient proof methods for more expressive and sophisticated extensions of SDL

A modal computational framework for default reasoning

Usually a default rule A : B/C is intended to mean that if A holds in a state of affairs a B is consistent, then C follows by default. However, C is not a necessary conclusion: different states of affairs are possible (conceivable). According to this view, Meyer and van der Hoek developed a multimodal logic, called S5P(n), for treating non-monotonic reasoning in a monotonic setting. In this paper we shall describe a proof search algorithm for S5P(n) which has been implemented as a Prolog Interpreter

Labelled Proofs For Quantified Modal Logic

We propose to extend description logic with defeasible rules, and to use the inferential mechanism of defeasible logic to reason with description logic constructors

An automated approach to normative reasoning

Deontic logic (DL) is increasingly recognized as an indispensable tool in such application areas as formal representation of legal knowledge and reasoning, formal specification of computer systems and formal analysis of database integrity constraints. Despite this acknowledgement, there have been few attempts to provide computationally tractable inference mechanisms for DL. In this paper we shall be concerned with providing a computationally oriented proof method for standard DL (SDL), i.e., normal systems of modal logic with the usual possible-worlds semantics. Because of the natural and easily implementable style of proof construction it uses, this method seems particularly well-suited for applications in the AI and Law field, and though in the present version it works for SDL only, it forms an appropriate basis for developing efficient proof methods for more expressive and sophisticated extensions of SDL

Ensaio sobre novas quest\uf5es filos\uf3ficas extra\ueddas do direito

Este artigo \ue9 uma homenagem a Leibniz e a sua obra da juventude Specimen quaestionum philosophicarum ex iure collectarum (\u201cEnsaio de quest\uf5es filo- s\uf3ficas extra\ueddas do direito\u201d). Neste texto, Leibniz, no in\uedcio de sua carreira como fil\uf3sofo e como jurista apresenta a sua (para a \ue9poca e provavelmente ainda hoje) tese audaciosa de que o direito se oferece espontaneamente \ue0 filosofia seja pelo que h\ue1 nele de intrinsecamente filos\uf3fico, seja porque \u201cmuit\uedssimos lugares do direito, sem a condu\ue7\ue3o desta, seriam um labirinto inextric\ue1vel\u201d. No rastro destas teses leibnizianas, o artigo se concentra em tr\ueas normas do ordenamento jur\ueddico italiano: o art. 1189 do C\uf3digo Civil italiano (pagamento ao credor aparente); o art. 47 del C\uf3digo Penal italiano (erro de fato), e o art. 533 do C\uf3digo de Processo Penal italiano (d\ufavida ra- zo\ue1vel). De cada um desses artigos \ue9 analisado o alcance filos\uf3fico impl\uedcito. O primeiro artigo nos leva diretamente ao problema da dicotomia entre realidade e apar\ueancia; o segundo p\uf5e o problema da nossa representa\ue7\ue3o da realidade, enquanto o terceiro levanta quest\uf5es acerca da diferen\ue7a entre d\ufavida poss\uedvel e d\ufavida razo\ue1vel. Em todos os tr\ueas casos s\ue3o tamb\ue9m sugeridas algumas poss\uedveis implica\ue7\uf5es jurisprudenciais da relativa leitura filos\uf3fica