Adaptive Logic Characterizations of Input/Output Logic

Abstract

Abstract.We translate unconstrained and constrained input/output logics as introduced by Makinson and van der Torre to modal logics, using adaptive logics for the constrained case. The resulting reformulation has some additional benefits. First, we obtain a prooftheoretic (dynamic) characterization of input/output logics. Second, we demonstrate that our framework naturally gives rise to useful variants and allows to express important notions that go beyond the expressive means of input/output logics, such as violations and sanctions.

Subordination Algebras as Semantic Environment of Input/Output Logic

“…We have presented a bi-modal characterization of input/output logic in the context of selfextensional logics, a class of logics defined in terms of minimal properties, which are satisfied both by classical propositional logic and by the best known nonclassical logics. The present approach is different from other modal formulations of input/output logic [25,29,35], also on a non-classical propositional base, in that the output operators themselves are semantically characterized as (suitable restrictions of) modal operators, and their properties characterized in terms of modal axioms (inequalities).…”

Reasoning With and About Norms in Logical Argumentation

“…It utilizes a correspondence between I/O and conditional logics. In [15] proof systems for constrained I/O logic are developed, where modalities for 'input' and 'output' allow for meta-reasoning in the object language. DAC uses labels instead of modalities and additionally allows for meta-reasoning about the (in)applicability of norms.…”

“…The second type of arguments concerns the nonmonotonicity of normative reasoning. The possibility to reason about the inapplicability of norms on the object language level distinguishes our work from other systems such as [14,15]. We illustrate the utility of our approach using the notion of related admissibility [16] to explain why some obligation holds despite certain norms to the contrary.…”

New Algebraic Normative Theories for Ethical and Legal Reasoning in the LogiKEy Framework

“…In this sense, we presented a semantical characterization for constrained I/O logic. There are syntactical ( [41], Section 6) and proof theoretical ( [42], Section 3) characterizations for constrained I/O logic. Our semantical characterization is more flexible than the syntactical characterization since our approach does not necessarily depend on the rules AND, SI, and (EQI, EQO) required for syntactic characterization of the I/O operations in modal logic [42].…”