The Story Model of Judicial Decision-Making and Reasoning With Evidence

The argumentative approach, the probability approach, and the story model are the three normative frameworks to reasoning with judicial evidence. The story model describes that judges reach the final conclusion by going through three different stages. The model also offered certainty principles, including evidential coverage, coherence, consistency, plausibility, and structural completeness to evaluate the stories. Different researchers have criticized the story model by pointing out that the model does not elaborate the meaning of evidential coverage and plausibility. Additionally, the story model has also been charged on the ground that it does not guide how to evaluate evidential coverage or plausibility of a story and how to select the best story when judges make more than one story. The present study demonstrates that these shortcomings may be overcome by using anchored narrative theory, causal abductive reasoning, story schemes, critical questions, and principles of inference to the best explanation.

VARIETIES OF POSITIVE MODAL ALGEBRAS AND STRUCTURAL COMPLETENESS

Positive modal algebras are the$$\left\langle { \wedge , \vee ,\diamondsuit ,\square,0,1} \right\rangle $$-subreducts of modal algebras. We prove that the variety of positive S4-algebras is not locally finite. On the other hand, the free one-generated positive S4-algebra is shown to be finite. Moreover, we describe the bottom part of the lattice of varieties of positive S4-algebras. Building on this, we characterize (passively, hereditarily) structurally complete varieties of positive K4-algebras.

UNIFICATION IN SUPERINTUITIONISTIC PREDICATE LOGICS AND ITS APPLICATIONS

We introduce unification in first-order logic. In propositional logic, unification was introduced by S. Ghilardi, see Ghilardi (1997, 1999, 2000). He successfully applied it in solving systematically the problem of admissibility of inference rules in intuitionistic and transitive modal propositional logics. Here we focus on superintuitionistic predicate logics and apply unification to some old and new problems: definability of disjunction and existential quantifier, disjunction and existential quantifier under implication, admissible rules, a basis for the passive rules, (almost) structural completeness, etc. For this aim we apply modified specific notions, introduced in propositional logic by Ghilardi, such as projective formulas, projective unifiers, etc.Unification in predicate logic seems to be harder than in the propositional case. Any definition of the key concept of substitution for predicate variables must take care of individual variables. We allow adding new free individual variables by substitutions (contrary to Pogorzelski & Prucnal (1975)). Moreover, since predicate logic is not as close to algebra as propositional logic, direct application of useful algebraic notions of finitely presented algebras, projective algebras, etc., is not possible.

Almost structural completeness; an algebraic approach

The notion of structural completeness has received considerable attention for many years. A translating to algebra gives: a quasivariety is structurally complete if it is generated by its free algebras. It appears that many deductive systems (quasivarieties), like S5 or MV<sub>n</sub> fails structural completeness for a rather immaterial reason. Therefore the adjusted notion was introduced: almost structural completeness. We investigate almost structural completeness from an algebraic perspective and obtain a characterization of this notion for quasivarieties.

Eartquake Vulnerability Level of Reconstructed Houses, Lesson Learned after Ten Years Java Eartquake 2006

Ten years after devastating earthquake May 27 th, 2006, housing reconstruction in the affected area has been done and development is still undergoing. Since then, houses are constructed in various forms and quality. Unrestrained housing development contributes uncertain quality of the buildings in term of building safety. This study examines the level of earthquake vulnerability on the reconstruction houses in the area according to the structural firmness. The method used is by assessing the structural completeness, especially the upper part of building elements, synchronized by the five damages classification for grouping the building affected by the quake. This method is aimed to predict damage level for the future similar earthquake. The outcome of this study shows the level of earthquake vulnerability in the every sub-district. It does also compare the level of building safety differences

PRESERVATION OF ADMISSIBLE RULES WHEN COMBINING LOGICS

Admissible rules are shown to be conservatively preserved by the meet-combination of a wide class of logics. A basis is obtained for the resulting logic from bases given for the component logics, under mild conditions. A weak form of structural completeness is proved to be preserved by the combination. Decidability of the set of admissible rules is also shown to be preserved, with no penalty on the time complexity. Examples are provided for the meet-combination of intermediate and modal logics.