The unification problem in a propositional logic is to determine, given formula φ, whether there exists substitution σ such that σ(φ) logic. In case, unifier of φ. When unifiable has minimal complete sets unifiers, it either infinitary, finitary, or unitary, depending on the cardinality its unifiers. Otherwise, nullary. this paper, we prove modal $\mathbf {K}+\square \square \bot $ , formulas a...

Methods for learning causal dependencies from observational data have been the focus of decades of work in social science, statistics, machine learning, and philosophy [9, 10, 11]. Much of the theoretical and practical work on causal discovery has focused on propositional representations. Propositional models effectively represent individual directed causal dependencies (e.g., path analysis, Ba...

Many classes of propositional calculus problems display a large amount of symmetries, i.e. the set of clauses representing such problems remains invariant under certain permutations of variable names. In [2,1] we have shown how such symmetries can be detected and used to simplify satis ability checking. The problem of nding all models of a given CNF propositional theory is known to be hard. Mor...

cross efficiency is a method with the idea of peer evaluation instead of self-evaluation, and is used for evaluation and ranking decision making units (dmus) in data envelopment analysis (dea). unlike most existing dea ranking models which can only rank a subset of dmus, for example non-efficient or extreme efficient dmus, cross efficiency can rank all dmus, even non-extreme ones. however, sinc...

Contemporary logic is confined to a few paradigmatic attitudes such as belief, knowledge, desire and intention. My purpose is to present a general modeltheoretical semantics of propositional attitudes of any cognitive or volitive mode. In my view, one can recursively define the set of all psychological modes of attitudes. As Descartes anticipated, the two primitive modes are those of belief and...

A ‘doxastic venture’ model of faith – according to which having faith involves believing beyond what is rationally justifiable – can be defended only on condition that such venturesome believing is both possible and ethically acceptable. I show how a development of the position argued by William James in ‘The will to believe ’ can succeed in meeting these conditions. A Jamesian defence of doxas...