781 research outputs found
A Parameterised Hierarchy of Argumentation Semantics for Extended Logic Programming and its Application to the Well-founded Semantics
Argumentation has proved a useful tool in defining formal semantics for
assumption-based reasoning by viewing a proof as a process in which proponents
and opponents attack each others arguments by undercuts (attack to an
argument's premise) and rebuts (attack to an argument's conclusion). In this
paper, we formulate a variety of notions of attack for extended logic programs
from combinations of undercuts and rebuts and define a general hierarchy of
argumentation semantics parameterised by the notions of attack chosen by
proponent and opponent. We prove the equivalence and subset relationships
between the semantics and examine some essential properties concerning
consistency and the coherence principle, which relates default negation and
explicit negation. Most significantly, we place existing semantics put forward
in the literature in our hierarchy and identify a particular argumentation
semantics for which we prove equivalence to the paraconsistent well-founded
semantics with explicit negation, WFSX. Finally, we present a general proof
theory, based on dialogue trees, and show that it is sound and complete with
respect to the argumentation semantics.Comment: To appear in Theory and Practice of Logic Programmin
A Paraconsistent Higher Order Logic
Classical logic predicts that everything (thus nothing useful at all) follows
from inconsistency. A paraconsistent logic is a logic where an inconsistency
does not lead to such an explosion, and since in practice consistency is
difficult to achieve there are many potential applications of paraconsistent
logics in knowledge-based systems, logical semantics of natural language, etc.
Higher order logics have the advantages of being expressive and with several
automated theorem provers available. Also the type system can be helpful. We
present a concise description of a paraconsistent higher order logic with
countable infinite indeterminacy, where each basic formula can get its own
indeterminate truth value (or as we prefer: truth code). The meaning of the
logical operators is new and rather different from traditional many-valued
logics as well as from logics based on bilattices. The adequacy of the logic is
examined by a case study in the domain of medicine. Thus we try to build a
bridge between the HOL and MVL communities. A sequent calculus is proposed
based on recent work by Muskens.Comment: Originally in the proceedings of PCL 2002, editors Hendrik Decker,
Joergen Villadsen, Toshiharu Waragai (http://floc02.diku.dk/PCL/). Correcte
Contradiction-tolerant process algebra with propositional signals
In a previous paper, an ACP-style process algebra was proposed in which
propositions are used as the visible part of the state of processes and as
state conditions under which processes may proceed. This process algebra,
called ACPps, is built on classical propositional logic. In this paper, we
present a version of ACPps built on a paraconsistent propositional logic which
is essentially the same as CLuNs. There are many systems that would have to
deal with self-contradictory states if no special measures were taken. For a
number of these systems, it is conceivable that accepting self-contradictory
states and dealing with them in a way based on a paraconsistent logic is an
alternative to taking special measures. The presented version of ACPps can be
suited for the description and analysis of systems that deal with
self-contradictory states in a way based on the above-mentioned paraconsistent
logic.Comment: 25 pages; 26 pages, occurrences of wrong symbol for bisimulation
equivalence replaced; 26 pages, Proposition 1 added; 27 pages, explanation of
the phrase 'in contradiction' added to section 2 and presentation of the
completeness result in section 2 improved; 27 pages, uniqueness result in
section 2 revised; 27 pages, last paragraph of section 8 revise
Real Islamic Logic
Four options for assigning a meaning to Islamic Logic are surveyed including
a new proposal for an option named "Real Islamic Logic" (RIL). That approach to
Islamic Logic should serve modern Islamic objectives in a way comparable to the
functionality of Islamic Finance. The prospective role of RIL is analyzed from
several perspectives: (i) parallel distributed systems design, (ii) reception
by a community structured audience, (iii) informal logic and applied
non-classical logics, and (iv) (in)tractability and artificial intelligence
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