Related papers: Aristotelian assertoric syllogistic
A new computational method that uses polynomial equations and dynamical systems to evaluate logical propositions is introduced and applied to Goedel's incompleteness theorems. The truth value of a logical formula subject to a set of axioms…
Finding solution values for unknowns in Boolean equations was a principal reasoning mode in the Algebra of Logic of the 19th century. Schr\"oder investigated it as Aufl\"osungsproblem (solution problem). It is closely related to the modern…
The likelihood of an automated reasoning program being of substantial assistance for a wide spectrum of applications rests with the nature of the options and parameters it offers on which to base needed strategies and methodologies. This…
The historiography of logic conceives of a Fregean revolution in which modern mathematical logic (also called symbolic logic) has replaced Aristotelian logic. The preeminent expositors of this conception are Jean van Heijenoort (1912-1986)…
In the 1950-ies P. F. Strawson proposed the Logic of Presuppositions. In this system sentences with empty subject are considered neither true nor false. Strawson considered only simple sentences with two predicate letters. But the concept…
Boolos's proof of incompleteness is extended straightforwardly to yield simple ``diagonalization-free'' proofs of some classical limitative theorems of logic.
The foundational character of certain algebraic structures as Boolean algebras and Heyting algebras is rooted in their potential to model classical and constructive logic, respectively. In this paper we discuss the contributions of…
Mathematical reasoning serves as a cornerstone for assessing the fundamental cognitive capabilities of human intelligence. In recent times, there has been a notable surge in the development of Large Language Models (LLMs) geared towards the…
Evidential reasoning is cast as the problem of simplifying the evidence-hypothesis relation and constructing combination formulas that possess certain testable properties. Important classes of evidence as identifiers, annihilators, and…
Neural language models trained with a predictive or masked objective have proven successful at capturing short and long distance syntactic dependencies. Here, we focus on verb argument structure in German, which has the interesting property…
Sequential propositional logic deviates from ordinary propositional logic by taking into account that during the sequential evaluation of a propositional statement,atomic propositions may yield different Boolean values at repeated…
We present a reading of the traditional syllogistics in a fragment of the propositional intuitionistic multiplicative linear logic and prove that with respect to a diagrammatic logical calculus that we introduced in a previous paper, a…
We consider a simple modal logic whose non-modal part has conjunction and disjunction as connectives and whose modalities come in adjoint pairs, but are not in general closure operators. Despite absence of negation and implication, and of…
We give sound and complete Hilbert-style axiomatizations for propositional dependence logic (PD), modal dependence logic (MDL), and extended modal dependence logic (EMDL) by extending existing axiomatizations for propositional logic and…
In this short note we relate some known properties of propositional calculus to purely algebraic considerations of a Boolean algebra. Classes of formulas of propositional calculus are considered as elements of a Boolean algebra. As such…
We consider the problem of answering queries about formulas of first-order logic based on background knowledge partially represented explicitly as other formulas, and partially represented as examples independently drawn from a fixed…
Given the large variety of existing logical formalisms it is of utmost importance to select the most adequate one for a specific purpose, e.g. for representing the knowledge relevant for a particular application or for using the formalism…
The Boolean satisfiability problem (SAT) is a well-known example of monotonic reasoning, of intense practical interest due to fast solvers, complemented by rigorous fine-grained complexity results. However, for non-monotonic reasoning,…
The logico-algebraic study of Lewis's hierarchy of variably strict conditional logics has been essentially unexplored, hindering our understanding of their mathematical foundations, and the connections with other logical systems. This work…
Competitive debaters often find themselves facing a challenging task -- how to debate a topic they know very little about, with only minutes to prepare, and without access to books or the Internet? What they often do is rely on "first…