Gaussoids are two-antecedental approximations of Gaussian conditional independence structures

The gaussoid axioms are conditional independence inference rules which characterize regular Gaussian CI structures over a three-element ground set. It is known that no finite set of inference rules completely describes regular Gaussian CI as the ground set grows. In this article we show that the gaussoid axioms logically imply every inference rule of at most two antecedents which is valid for regular Gaussians over any ground set. The proof is accomplished by exhibiting for each inclusion-minimal gaussoid extension of at most two CI statements a regular Gaussian realization. Moreover we prove that all those gaussoids have rational positive-definite realizations inside every ε-ball around the identity matrix. For the proof we introduce the concept of algebraic Gaussians over arbitrary fields and of positive Gaussians over ordered fields and obtain the same two-antecedental completeness of the gaussoid axioms for algebraic and positive Gaussians over all fields of characteristic zero as a byproduct.

Fictional truth

A well-known theory about under which circumstances a statement is true in a fiction is the Reality Principle (RP), which originates in the work of David Lewis: “(RP) Where p1…pn are the primary fictional truths of a fiction F, it is true in F that q iff the following holds: were p1…pn the case, q would have been the case” (Walton 1990, 44). RP has been subjected to a number of counterexamples, up to a point where, in the words of Stacie Friend (2017, 33), “it is widely recognized that the Reality Principle […] cannot be a universal inference rule for implied story-truths”. This chapter argues that the strength of these counterexamples is widely overestimated, and that they do not, on closer scrutiny, constitute reasons for rejecting RP.

On Basic Probability Logic Inequalities

We give some simple examples of applying some of the well-known elementary probability theory inequalities and properties in the field of logical argumentation. A probabilistic version of the hypothetical syllogism inference rule is as follows: if propositions A, B, C, A→B, and B→C have probabilities a, b, c, r, and s, respectively, then for probability p of A→C, we have f(a,b,c,r,s)≤p≤g(a,b,c,r,s), for some functions f and g of given parameters. In this paper, after a short overview of known rules related to conjunction and disjunction, we proposed some probabilized forms of the hypothetical syllogism inference rule, with the best possible bounds for the probability of conclusion, covering simultaneously the probabilistic versions of both modus ponens and modus tollens rules, as already considered by Suppes, Hailperin, and Wagner.

Equational Theorem Proving Modulo

Unlike other methods for theorem proving modulo with constrained clauses [12, 13], equational theorem proving modulo with constrained clauses along with its simplification techniques has not been well studied. We introduce a basic paramodulation calculus modulo equational theories E satisfying certain properties of E and present a new framework for equational theorem proving modulo E with constrained clauses. We propose an inference rule called Generalized E-Parallel for constrained clauses, which makes our inference system completely basic, meaning that we do not need to allow any paramodulation in the constraint part of a constrained clause for refutational completeness. We present a saturation procedure for constrained clauses based on relative reducibility and show that our inference system including our contraction rules is refutationally complete.

Admissible Inference Rules and Semantic Property of Modal Logics

Firstly semantic property of nonstandart logics were described by formulas which are peculiar to studied a models in general, and do not take to consideration a variable conditions and a changing assumptions. Evidently the notion of inference rule generalizes the notion of formulas and brings us more flexibility and more expressive power to model human reasoning and computing. In 2000-2010 a few results on describing of explicit bases for admissible inference rules for nonstandard logics (S4, K4, H etc.) appeared. The key property of these logics was weak co-cover property. Beside the improvement of deductive power in logic, an admissible rule are able to describe some semantic property of given logic. We describe a semantic property of modal logics in term of admissibility of given set of inference rules. We prove that modal logic over logic 𝐺𝐿 enjoys weak co-cover property iff all given rules are admissible for logic.

Der Kettenschluss – eine Verteidigung

Proponents of conditional logics such as David Lewis and Robert Stalnaker reject inferences containing counterfactuals from "if A, B" and "if B, C" to "if A, C" due to ordinary language counterexamples. Contextualists defend this inference rule called "hypothetical syllogism" or "transitivity" on the basis of a possible word semantics, which, however, assigns implausible truth values to certain counterfactuals. My defence of hypothetical syllogism avoids this problem, as it rests on Nelson Goodman's uncontroversial, metaphysically parsimonious assumption that we accept counterfactuals as true only under certain conditions from which, in conjunction with the antecedent, the consequent can be inferred. The counterexamples to hypothetical syllogism can be rebutted because their premises are doxastically noncotenable; that is, there is no set of conditions under which the premises can be accepted as jointly true.

Linguistic Conventions

What are linguistic conventions? This chapter begins by noting and setting aside philosophical accounts of social conventions stemming from Lewis’s influential treatment. It then criticizes accounts that see conventions as explicit stipulations. From there the chapter argues that conventions are syntactic rules of inference, arguing that there are scientific reasons to posit these rules as part of our linguistic competence and that we need to include both bilateralist and open-ended inference rules for a full account. The back half of the chapter aims to naturalize inference rule-following by providing functionalist-dispositionalist approaches to our attitudes, inference, and inference-rule–following, addressing Kripkenstein’s arguments and several other concerns along the way.

Searching and describing objects in satellite images on the basis of modeling reasoning

The article presents an approach to a problem of contextual search and description of objects in raster satellite images, which consists in modeling reasoning on the basis of structured cases. As a result of image processing, an adjacency graph of color regions is constructed. The object is characterized by color, attributes of the form of segments of the border and the shape of the object as a whole. A structured case is represented in the form of a beam graph, whose arcs are ordered according to a positive bypass of the region boundaries. Using a graph matching algorithm, occurrences of cases stored in the system database are detected in the analyzed image. When the occurrence is detected, a case-based inference rule is applied. The degree to which an object belongs to a certain class depends not only on the properties of the object itself, but also on the reliability of the surrounding objects. The contextual search strategy contains stages of recursion and iteration. In contrast to neural network technologies, the proposed approach allows one not only to classify image objects, but also to form their structured descriptions. In addition, the classification decision issued by the system has a reasoned justification. The results of the experiment show that reasoning based on structured cases allows refining the results of classification and increasing the reliability of object recognition in satellite images.