Search

The similarity between logic and semantics of the Stoics and Frege has long been known, and it can be explained in various ways. In 2021, Susane Bobzien published a work in which she explains this similarity rather surprisingly: she hypothesizes that Frege generously helped himself with the foundations of Stoic logic as it was published in the first volume of History of Logic in the West by Carl Prantl. However, this hypothesis encounters various problems. The key point of the whole accusation is founded on the formulation of a general proposition in language using implication and anaphora, which Frege supposedly took from the Stoics, although in Prantl's text there is only one example of a sentence with this structure. On the contrary, there are many examples of such sentences in contemporary professional (e.g. legal) texts. Many examples of semantic similarities that Bobzien presents are based only on the similarities between isolated concepts; however, that is regularly the case for such concepts with the same conceptual basis. Bobzien presents a significant number of matches only on the basis of results that could allegedly be inferred from the texts. However, this cannot be considered a proof of plagiarism. Bobzien does not consider many sources for the continuity of interpretation such as the so-called hypothetical syllogism found in available textbooks of logic. Last but not least, her claims do not consider many differences between Stoic and Frege's logic. All this leads us to the conclusion that Bobzien does not present sufficient facts and connections between them that would confirm her hypothesis about Frege's plagiarism of the Stoic logic: Frege simply was not a plagiarist. [ABSTRACT FROM AUTHOR]

This paper analyzes the logic deduction and reasoning techniques used in several intelligent decision support algorithms, and proposes a flexible planning method GARIv using fuzzy descriptive logic in media enterprise management. Combined with experiments, the above methods are illustrated in terms of effectiveness and feasibility. In the end, the challenges and possible solutions of intelligent decision support algorithms with self-adaption reasoning are discussed. [ABSTRACT FROM AUTHOR]

The modal characterization theorem by J. van Benthem characterizes classical modal logic as the bisimulation invariant fragment of first-order logic. In this paper, we prove a similar characterization theorem for intuitionistic modal logic. For this purpose we introduce the notion of modal asimulation as an analogue of bisimulations. The paper treats four different fragments of first-order logic induced by their respective versions of Kripke-style semantics for modal intuitionistic logic. It is shown further that this characterization can be easily carried over to arbitrary first-order definable subclasses of classical first-order models. [ABSTRACT FROM AUTHOR]

This paper presents a version of belief function theory in which masses are assigned to propositional formulas and which allows the modeler to consider integrity constraints. It also provides three combination rules which apply within this framework. It proves that the initial version of belief function theory and its extension to non-exclusive hypotheses are two particular cases of this proposal. It finally shows that, even if this framework is not more expressive than the belief function theory as defined by Dempster and Shafer, its interest resides in the fact that it offers the modeler a rich language to express its beliefs, i.e., the propositional language. [ABSTRACT FROM AUTHOR]

This work was intended to be an attempt to introduce the metalanguage for working with multiple-conclusion inference rules that admit asserted propositions along with the rejected propositions. The presence of rejected propositions, and especially the presence of the rule of reverse substitution, requires certain change the definition of structurality. [ABSTRACT FROM AUTHOR]

We investigate how to formalize reasoning that takes account of time by using connectives like "before" and "after." We develop semantics for a formal logic, which we axiomatize. In proving that the axiomatization is strongly complete we show how a temporal ordering of propositions can yield a linear timeline. We formalize examples of ordinary language sentences to illustrate the scope and limitations of this method. We then discuss ways to deal with some of those limitations. [ABSTRACT FROM AUTHOR]

In this paper we survey different methods of computation of prime implicants and implicates in propositional, first order and modal logic and their applications in electrical engineering, truth maintenance systems and Diagnosis. [ABSTRACT FROM AUTHOR]

Abstract: Knowledge about complex events is usually incomplete in practice. We distinguish between random variables that can be assigned a designated marker to model missing data values, and certain random variables to which the designated marker cannot be assigned. The ability to specify an arbitrary set of certain random variables provides an effective mechanism to control the uncertainty in form of missing data values. A finite axiomatization for the implication problem of saturated conditional independence statements is established under controlled uncertainty, relative to discrete probability measures. The completeness proof utilizes special probability models where two assignments have probability one half. The special probability models enable us to establish an equivalence between the implication problem and that of a propositional fragment in Cadoli and Schaerfʼs -3 logic. Here, the propositional variables in correspond to the random variables specified to be certain. The duality leads to an almost linear time algorithm to decide implication. It is shown that this duality cannot be extended to cover general conditional independence statements. All results subsume classical reasoning about saturated conditional independence statements as the idealized special case where every random variable is certain. Under controlled uncertainty, certain random variables allow us to soundly approximate classical reasoning about saturated conditional independence statements. [Copyright &y& Elsevier]

Abstract: We begin by offering a new, direct proof of the equivalence between the problem of the existence of kernels in digraphs, KER, and satisfiability of propositional theories, SAT, giving linear reductions in both directions. Having introduced some linear reductions of the input graph, we present new algorithms for KER, with variations utilizing solvers of boolean equations. In the worst case, the algorithms try all assignments to either a feedback vertex set, F, or a set of nodes E touching only all even cycles. Hence KER is fixed parameter tractable not only in the size of F, as observed earlier, but also in the size of E. A slight modification of these algorithms leads to a branch and bound algorithm for KER which is virtually identical to the DPLL algorithm for SAT. This suggests deeper analogies between the two problems and the probable scenario of KER research facing the challenges known from the work on SAT. The algorithm gives also the upper bound on the time complexity of general KER and of KER for oriented graphs, where is the number of vertices. [Copyright &y& Elsevier]

Typically, before association rules are mined, a user needs to determine a support threshold in order to obtain only the frequent item sets. Having users to determine a support threshold attracts a number of issues. We propose an association rule mining framework that does not require a pre-set support threshold. The framework is developed based on implication of propositional logic. The experiments show that our approach is able to identify meaningful association rules within an acceptable execution time. [ABSTRACT FROM AUTHOR]