1,377 research outputs found
A cognitive view of relevant implication
Relevant logics provide an alternative to classical implication
that is capable of accounting for the relationship between the antecedent
and the consequence of a valid implication. Relevant implication is usually
explained in terms of information required to assess a proposition.
By doing so, relevant implication introduces a number of cognitively relevant
aspects in the denition of logical operators. In this paper, we
aim to take a closer look at the cognitive feature of relevant implication.
For this purpose, we develop a cognitively-oriented interpretation of the
semantics of relevant logics. In particular, we provide an interpretation
of Routley-Meyer semantics in terms of conceptual spaces and we show
that it meets the constraints of the algebraic semantics of relevant logic
On Constructive Connectives and Systems
Canonical inference rules and canonical systems are defined in the framework
of non-strict single-conclusion sequent systems, in which the succeedents of
sequents can be empty. Important properties of this framework are investigated,
and a general non-deterministic Kripke-style semantics is provided. This
general semantics is then used to provide a constructive (and very natural),
sufficient and necessary coherence criterion for the validity of the strong
cut-elimination theorem in such a system. These results suggest new syntactic
and semantic characterizations of basic constructive connectives
Automated Synthesis of Tableau Calculi
This paper presents a method for synthesising sound and complete tableau
calculi. Given a specification of the formal semantics of a logic, the method
generates a set of tableau inference rules that can then be used to reason
within the logic. The method guarantees that the generated rules form a
calculus which is sound and constructively complete. If the logic can be shown
to admit finite filtration with respect to a well-defined first-order semantics
then adding a general blocking mechanism provides a terminating tableau
calculus. The process of generating tableau rules can be completely automated
and produces, together with the blocking mechanism, an automated procedure for
generating tableau decision procedures. For illustration we show the
workability of the approach for a description logic with transitive roles and
propositional intuitionistic logic.Comment: 32 page
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