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The Pleadings Game  An Artificial Intelligence Model of Procedural Justice
, 1993
"... One of the central questions of legal philosophy concerns the division of power between the judicial and legislative branches of government: where is the border between a judge's power to decide cases by applying the law, and the legislature's power to create law? How should it be decided whether or ..."
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Cited by 103 (8 self)
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One of the central questions of legal philosophy concerns the division of power between the judicial and legislative branches of government: where is the border between a judge's power to decide cases by applying the law, and the legislature's power to create law? How should it be decided whether or not a judge has exceeded the limits of his discretion? The Pleadings Game is a normative formalization and computational model of legal reasoning and argumentation intended to help answer these questions. In the prominent theory of H.L.A. Hart, judicial discretion is limited by the literal meaning of legislation. To use the standard example, if a law prohibits vehicles from a park, according to Hart's theory a judge would not have discretion to permit a military tank, even if intended to be used as a war memorial. The Pleadings Game is based on another approach, Robert Alexy's discourse theory of legal argumentation. Alexy views legal reasoning as a rule governed language game, where the r...
The ProofTheory and Semantics of Intuitionistic Modal Logic
, 1994
"... Possible world semantics underlies many of the applications of modal logic in computer science and philosophy. The standard theory arises from interpreting the semantic definitions in the ordinary metatheory of informal classical mathematics. If, however, the same semantic definitions are interpret ..."
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Cited by 100 (0 self)
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Possible world semantics underlies many of the applications of modal logic in computer science and philosophy. The standard theory arises from interpreting the semantic definitions in the ordinary metatheory of informal classical mathematics. If, however, the same semantic definitions are interpreted in an intuitionistic metatheory then the induced modal logics no longer satisfy certain intuitionistically invalid principles. This thesis investigates the intuitionistic modal logics that arise in this way. Natural deduction systems for various intuitionistic modal logics are presented. From one point of view, these systems are selfjustifying in that a possible world interpretation of the modalities can be read off directly from the inference rules. A technical justification is given by the faithfulness of translations into intuitionistic firstorder logic. It is also established that, in many cases, the natural deduction systems induce wellknown intuitionistic modal logics, previously given by Hilbertstyle axiomatizations. The main benefit of the natural deduction systems over axiomatizations is their
Logics of Formal Inconsistency
 Handbook of Philosophical Logic
"... 1.1 Contradictoriness and inconsistency, consistency and noncontradictoriness In traditional logic, contradictoriness (the presence of contradictions in a theory or in a body of knowledge) and triviality (the fact that such a theory ..."
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Cited by 45 (19 self)
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1.1 Contradictoriness and inconsistency, consistency and noncontradictoriness In traditional logic, contradictoriness (the presence of contradictions in a theory or in a body of knowledge) and triviality (the fact that such a theory
A characterization of strong equivalence for logic programs with variables
 In: Proc. of the 9th Intl. Conf. on Logic Programming and Nonmonotonic Reasoning
, 2007
"... a valverdectima.uma.es Abstract. Two sets of rules are said to be strongly equivalent to each other if replacing one by the other within any logic program preserves the program's stable models. The familiar characterization of strong equivalence of grounded programs in terms of the propositional log ..."
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Cited by 30 (21 self)
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a valverdectima.uma.es Abstract. Two sets of rules are said to be strongly equivalent to each other if replacing one by the other within any logic program preserves the program's stable models. The familiar characterization of strong equivalence of grounded programs in terms of the propositional logic of hereandthere is extended in this paper to a large class of logic programs with variables. This class includes, in particular, programs with conditional literals and cardinality constraints. The firstorder version of the logic of hereandthere required for this purpose involves two additional nonintuitionistic axiom schemas.
The Logic of Justification
 Cornell University
, 2008
"... We describe a general logical framework, Justification Logic, for reasoning about epistemic justification. Justification Logic is based on classical propositional logic augmented by justification assertions t:F that read t is a justification for F. Justification Logic absorbs basic principles origin ..."
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Cited by 30 (4 self)
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We describe a general logical framework, Justification Logic, for reasoning about epistemic justification. Justification Logic is based on classical propositional logic augmented by justification assertions t:F that read t is a justification for F. Justification Logic absorbs basic principles originating from both mainstream epistemology and the mathematical theory of proofs. It contributes to the studies of the wellknown Justified True Belief vs. Knowledge problem. We state a general Correspondence Theorem showing that behind each epistemic modal logic, there is a robust system of justifications. This renders a new, evidencebased foundation for epistemic logic. As a case study, we offer a resolution of the GoldmanKripke ‘Red Barn ’ paradox and analyze Russell’s ‘prime minister example ’ in Justification Logic. Furthermore, we formalize the wellknown Gettier example and reveal hidden assumptions and redundancies in Gettier’s reasoning. 1
On Bunched Predicate Logic
 Proceedings of the IEEE Symposium on Logic in Computer Science
, 1999
"... We present the logic of bunched implications, BI, in which a multiplicative (or linear) and an additive (or intuitionistic) implication live sidebyside. The propositional version of BI arises from an analysis of the prooftheoretic relationship between conjunction and implication, and may be viewe ..."
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Cited by 29 (17 self)
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We present the logic of bunched implications, BI, in which a multiplicative (or linear) and an additive (or intuitionistic) implication live sidebyside. The propositional version of BI arises from an analysis of the prooftheoretic relationship between conjunction and implication, and may be viewed as a merging of intuitionistic logic and multiplicative, intuitionistic linear logic. The predicate version of BI includes, in addition to usual additive quantifiers, multiplicative (or intensional) quantifiers 8new and 9new , which arise from observing restrictions on structural rules on the level of terms as well as propositions. Moreover, these restrictions naturally allow the distinction between additive predication and multiplicative predication for each propositional connective. We provide a natural deduction system, a sequent calculus, a Kripke semantics and a BHK semantics for BI. We mention computational interpretations, based on locality and sharing, at both the propositiona...
Provability logic
 Handbook of Philosophical Logic, 2nd ed
, 2004
"... We describe a general logical framework, Justification Logic, for reasoning about epistemic justification. Justification Logic is based on classical propositional logic augmented by justification assertions t:F that read t is a justification for F. Justification Logic absorbs basic principles origin ..."
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Cited by 25 (9 self)
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We describe a general logical framework, Justification Logic, for reasoning about epistemic justification. Justification Logic is based on classical propositional logic augmented by justification assertions t:F that read t is a justification for F. Justification Logic absorbs basic principles originating from both mainstream epistemology and the mathematical theory of proofs. It contributes to the studies of the wellknown Justified True Belief vs. Knowledge problem. As a case study, we formalize Gettier examples in Justification Logic and reveal hidden assumptions and redundancies in Gettier reasoning. We state a general Correspondence Theorem showing that behind each epistemic modal logic, there is a robust system of justifications. This renders a new, evidencebased foundation for epistemic logic. 1
Subtractive Logic
, 1999
"... This paper is the first part of a work whose purpose is to investigate duality in some related frameworks (cartesian closed categories, lambdacalculi, intuitionistic and classical logics) from syntactic, semantical and computational viewpoints. We start with category theory and we show that any ..."
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Cited by 20 (1 self)
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This paper is the first part of a work whose purpose is to investigate duality in some related frameworks (cartesian closed categories, lambdacalculi, intuitionistic and classical logics) from syntactic, semantical and computational viewpoints. We start with category theory and we show that any bicartesian closed category with coexponents is degenerated (i.e. there is at most one arrow between two objects). The remainder of the paper is devoted to logical issues. We examine the propositional calculus underlying the type system of bicartesian closed categories with coexponents and we show that this calculus corresponds to subtractive logic: a conservative extension of intuitionistic logic with a new connector (subtraction) dual to implication. Eventually, we consider first order subtractive logic and we present an embedding of classical logic into subtractive logic. Introduction This paper is the first part of a work whose purpose is to investigate duality in some related ...
FirstOrder Logic of Proofs
, 2011
"... The propositional logic of proofs LP revealed an explicit provability reading of modal logic S4 which provided an indented provability semantics for the propositional intuitionistic logic IPC and led to a new area, Justification Logic. In this paper, we find the firstorder logic of proofs FOLP capa ..."
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Cited by 20 (9 self)
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The propositional logic of proofs LP revealed an explicit provability reading of modal logic S4 which provided an indented provability semantics for the propositional intuitionistic logic IPC and led to a new area, Justification Logic. In this paper, we find the firstorder logic of proofs FOLP capable of realizing firstorder modal logic S4 and, therefore, the firstorder intuitionistic logic HPC. FOLP enjoys a natural provability interpretation; this provides a semantics of explicit proofs for firstorder S4 and HPC compliant with BrouwerHeytingKolmogorov requirements. FOLP opens the door to a general theory of firstorder justification.
On the Insufficiency of Ontologies: Problems in Knowledge Sharing and Alternative Solutions
"... One of the benefits of formally represented knowledge lies in its potential to be shared. Ontologies have been proposed as the ultimate solution to problems in knowledge sharing. However even when an agreed correspondence between ontologies is reached that is not the end of the problems in knowledge ..."
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Cited by 18 (1 self)
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One of the benefits of formally represented knowledge lies in its potential to be shared. Ontologies have been proposed as the ultimate solution to problems in knowledge sharing. However even when an agreed correspondence between ontologies is reached that is not the end of the problems in knowledge sharing. In this paper we explore a number of realistic knowledgesharing situations and their related problems for which ontologies fall short in providing a solution. For each situation we propose and analyse alternative solutions.