5,461 research outputs found
Modelling Value-Oriented Legal Reasoning in LogiKEy
The logico-pluralist LogiKEy knowledge engineering methodology and framework is applied to the modelling of a theory of legal balancing, in which legal knowledge (cases and laws) is encoded by utilising context-dependent value preferences. The theory obtained is then used to formalise, automatically evaluate, and reconstruct illustrative property law cases (involving the appropriation of wild animals) within the Isabelle/HOL proof assistant system, illustrating how LogiKEy can harness interactive and automated theorem-proving technology to provide a testbed for the development and formal verification of legal domain-specific languages and theories. Modelling value-oriented legal reasoning in that framework, we establish novel bridges between the latest research in knowledge representation and reasoning in non-classical logics, automated theorem proving, and applications in legal reasoning
Designing Normative Theories for Ethical and Legal Reasoning: LogiKEy Framework, Methodology, and Tool Support
A framework and methodology---termed LogiKEy---for the design and engineering
of ethical reasoners, normative theories and deontic logics is presented. The
overall motivation is the development of suitable means for the control and
governance of intelligent autonomous systems. LogiKEy's unifying formal
framework is based on semantical embeddings of deontic logics, logic
combinations and ethico-legal domain theories in expressive classic
higher-order logic (HOL). This meta-logical approach enables the provision of
powerful tool support in LogiKEy: off-the-shelf theorem provers and model
finders for HOL are assisting the LogiKEy designer of ethical intelligent
agents to flexibly experiment with underlying logics and their combinations,
with ethico-legal domain theories, and with concrete examples---all at the same
time. Continuous improvements of these off-the-shelf provers, without further
ado, leverage the reasoning performance in LogiKEy. Case studies, in which the
LogiKEy framework and methodology has been applied and tested, give evidence
that HOL's undecidability often does not hinder efficient experimentation.Comment: 50 pages; 10 figure
Semantical Investigations on Non-classical Logics with Recovery Operators: Negation
We investigate mathematical structures that provide a natural semantics for
families of (quantified) non-classical logics featuring special unary
connectives, called recovery operators, that allow us to 'recover' the
properties of classical logic in a controlled fashion. These structures are
called topological Boolean algebras. They are Boolean algebras extended with
additional unary operations, called operators, such that they satisfy
particular conditions of a topological nature. In the present work we focus on
the paradigmatic case of negation. We show how these algebras are well-suited
to provide a semantics for some families of paraconsistent Logics of Formal
Inconsistency and paracomplete Logics of Formal Undeterminedness, which feature
recovery operators used to earmark propositions that behave 'classically' in
interaction with non-classical negations. In contrast to traditional semantical
investigations, carried out in natural language (extended with mathematical
shorthand), our formal meta-language is a system of higher-order logic (HOL)
for which automated reasoning tools exist. In our approach, topological Boolean
algebras become encoded as algebras of sets via their Stone-type
representation. We employ our higher-order meta-logic to define and interrelate
several transformations on unary set operations (operators), which naturally
give rise to a topological cube of opposition. Furthermore, our approach allows
for a uniform characterization of propositional, first-order and higher-order
quantification (also restricted to constant and varying domains). With this
work we want to make a case for the utilization of automated theorem proving
technology for doing computer-supported research in non-classical logics. All
presented results have been formally verified (and in many cases obtained)
using the Isabelle/HOL proof assistant
Automatic Generation of Proof Tactics for Finite-Valued Logics
A number of flexible tactic-based logical frameworks are nowadays available
that can implement a wide range of mathematical theories using a common
higher-order metalanguage. Used as proof assistants, one of the advantages of
such powerful systems resides in their responsiveness to extensibility of their
reasoning capabilities, being designed over rule-based programming languages
that allow the user to build her own `programs to construct proofs' - the
so-called proof tactics.
The present contribution discusses the implementation of an algorithm that
generates sound and complete tableau systems for a very inclusive class of
sufficiently expressive finite-valued propositional logics, and then
illustrates some of the challenges and difficulties related to the algorithmic
formation of automated theorem proving tactics for such logics. The procedure
on whose implementation we will report is based on a generalized notion of
analyticity of proof systems that is intended to guarantee termination of the
corresponding automated tactics on what concerns theoremhood in our targeted
logics
Deciding regular grammar logics with converse through first-order logic
We provide a simple translation of the satisfiability problem for regular
grammar logics with converse into GF2, which is the intersection of the guarded
fragment and the 2-variable fragment of first-order logic. This translation is
theoretically interesting because it translates modal logics with certain frame
conditions into first-order logic, without explicitly expressing the frame
conditions.
A consequence of the translation is that the general satisfiability problem
for regular grammar logics with converse is in EXPTIME. This extends a previous
result of the first author for grammar logics without converse. Using the same
method, we show how some other modal logics can be naturally translated into
GF2, including nominal tense logics and intuitionistic logic.
In our view, the results in this paper show that the natural first-order
fragment corresponding to regular grammar logics is simply GF2 without extra
machinery such as fixed point-operators.Comment: 34 page
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