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In Pietroski (2018) a simple representation language called SMPL is introduced, construed as a hypothesis about core conceptual structure. The present work is a study of this system from a logical perspective. In addition to establishing a completeness result and a complexity characterization for reasoning in the system, we also pinpoint its expressive limits, in particular showing that the fourth corner in the square of opposition ("Some_not") eludes expression. We then study a seemingly small extension, called SMPL+, which allows for a minimal predicate-binding operator. Perhaps surprisingly, the resulting system is shown to encode precisely the concepts expressible in first-order logic. However, unlike the latter class, the class of SMPL+ expressions admits a simple procedural (context-free) characterization. Our contribution brings together research strands in logic—including natural logic, modal logic, description logic, and hybrid logic—with recent advances in semantics and philosophy of language. [ABSTRACT FROM AUTHOR]

This paper explores relational syllogistic logics, a family of logical systems related to reasoning about relations in extensions of the classical syllogistic. These are all decidable logical systems. We prove completeness theorems and complexity results for a natural subfamily of relational syllogistic logics, parametrized by constructors for terms and for sentences. [ABSTRACT FROM AUTHOR]

This article enlarges classical syllogistic logic with assertions having to do with comparisons between the sizes of sets. So it concerns a logical system whose sentences are of the following forms: All x are y and Some x are y , There are at least as many x as y , and There are more x than y. Here x and y range over subsets (not elements) of a given infinite set. Moreover, x and y may appear complemented (i.e., as x and ӯ), with the natural meaning. We formulate a logic for our language that is based on the classical syllogistic. The main result is a soundness/completeness theorem. There are efficient algorithms for proof search and model construction. [ABSTRACT FROM AUTHOR]

We add Most X are Y to the syllogistic logic of All X are Y and Some X are Y. We prove soundness, completeness, and decidability in polynomial time. Our logic has infinitely many rules, and we prove that this is unavoidable. [ABSTRACT FROM AUTHOR]

Discusses the concept of quantum logic in relation to quantum computing. Variation in the definition of quantum logic; Consideration of the lattice of closed subspaces of a Hilbert space; Theoretical basis of quantum computing; Observation that quantum logic is not a finite-valued logic; Illustration of some open problems.

Discusses analogs of the frame correspondence results for models. In-depth look at a basic result for infinitary modal logic; Examination of classes of model-world pairs closed under bisimulation; Qualities of infinitary modal logic.