8 research outputs found
A New Algorithmic Decision for Categorical Syllogisms via Caroll's Diagrams
In this paper, we deal with a calculus system SLCD (Syllogistic Logic with
Carroll Diagrams), which gives a formal approach to logical reasoning with
diagrams, for representations of the fundamental Aristotelian categorical
propositions and show that they are closed under the syllogistic criterion of
inference which is the deletion of middle term. Therefore, it is implemented to
let the formalism comprise synchronically bilateral and trilateral
diagrammatical appearance and a naive algorithmic nature. And also, there is no
need specific knowledge or exclusive ability to understand as well as to use
it. Consequently, we give an effective algorithm used to determine whether a
syllogistic reasoning valid or not by using SLCD
A system of relational syllogistic incorporating full Boolean reasoning
We present a system of relational syllogistic, based on classical
propositional logic, having primitives of the following form:
Some A are R-related to some B;
Some A are R-related to all B;
All A are R-related to some B;
All A are R-related to all B.
Such primitives formalize sentences from natural language like `All students
read some textbooks'. Here A and B denote arbitrary sets (of objects), and R
denotes an arbitrary binary relation between objects. The language of the logic
contains only variables denoting sets, determining the class of set terms, and
variables denoting binary relations between objects, determining the class of
relational terms. Both classes of terms are closed under the standard Boolean
operations. The set of relational terms is also closed under taking the
converse of a relation. The results of the paper are the completeness theorem
with respect to the intended semantics and the computational complexity of the
satisfiability problem.Comment: Available at
http://link.springer.com/article/10.1007/s10849-012-9165-
A Note on the Complexity of the Satisfiability Problem for Graded Modal Logics
Graded modal logic is the formal language obtained from ordinary
(propositional) modal logic by endowing its modal operators with cardinality
constraints. Under the familiar possible-worlds semantics, these augmented
modal operators receive interpretations such as "It is true at no fewer than 15
accessible worlds that...", or "It is true at no more than 2 accessible worlds
that...". We investigate the complexity of satisfiability for this language
over some familiar classes of frames. This problem is more challenging than its
ordinary modal logic counterpart--especially in the case of transitive frames,
where graded modal logic lacks the tree-model property. We obtain tight
complexity bounds for the problem of determining the satisfiability of a given
graded modal logic formula over the classes of frames characterized by any
combination of reflexivity, seriality, symmetry, transitivity and the Euclidean
property.Comment: Full proofs for paper presented at the IEEE Conference on Logic in
Computer Science, 200
On the computational complexity of the numerically definite syllogistic and related logics
In this paper, we determine the complexity of the satisfiability problem for various logics obtained by adding numerical quantifiers, and other constructions, to the traditional syllogistic. In addition, we demonstrate the incompleteness of some recently proposed proof-systems for these logics.