Разрешимость многоагентной логики деревьев вычислений 𝒞𝒯 ℒ𝒦𝑅𝑒𝑙

To make sense of an utterance, people identify in its linear linguistic expression the concepts and the connections between them. A concept normally has a lexical realization; connections between concepts often do not, but they are perceived even without the benefit of lexical cues. Making these connections – called semantic relations in the field of natural language processing – relies on the form and structure of linguistic expressions, and the concepts these expressions evoke. This implies two levels: the level of the text, the linguistic expression with its form and (grammatical) structure, and the level of the concepts which the speaker wants to convey.
 An overview of the literature shows that semantic relations are, for pragmatic reasons, a means to an end – extract information, explain the links between the head of a phrase and its arguments, and so on – and that is why they are analyzed from the perspective of what they link. At the text level, the process of semantic relation analysis is informed by syntactic elements – noun phrases, verbs and their arguments, clauses and so on – thus differentiating semantic relations based on the complexity of the syntactic constructions in which their arguments appear. At the conceptual level, the same semantic relation is assigned to pairs of concepts, regardless of their surface expression. The process can be said to disregard the implications of having syntactic constructions of various complexity correspond to the concepts linked.
 In this article, we propose to put semantic relations first: analyze them, determine what constraints they place on the concepts they connect, and how those concepts can be lexicalized. Lexicalization takes place via expressions of increasing syntactic complexity: phrases, clauses and multi-clause sentences. Next, we show how the linguistic phenomena involved in producing different lexicalizations explain – in a systematic manner – how semantic relations can have instances in syntactic constructions of various complexity. We focus on binary semantic relations between concepts/textual elements within sentences.
 This kind of analysis leads to a better understanding of the relations themselves and to a systematic account of phenomena related to their occurrence in texts. It reveals some of the assumptions and linguistic gaps people fill when they recognize relations in text. From the computational point of view of text processing, such a solid basis of the analysis of semantic relations adds consistency. Evidence for a particular relation can come from all its instances in a text, regardless of the syntactic form of the concepts it connects. Knowledge of the expected concepts and their syntactic realization may signal the presence of covert or implied information, which we can then work to retrieve. Assigning a semantic relation should be a conscious choice, with the understanding of what implications such a tag has both for the implicitly and explicitly expressed elements of a concept.

The discussion so far has been employing the notion of possible worlds, popularized via the semantics of modal logic. How seriously, however, should possible worlds be taken? David Lewis held them to be genuine, concrete worlds, no less real than ours, the actual world, whereas Robert Stalnaker and Saul Kripke take them to be, rather, abstract entities, properties of the actual world—the only real world—which it might possibly possess. I agree with Lewis that possible worlds are no less real than the actual world, but I also agree with Stalnaker that only our world actually exists. I affirm that merely possible worlds, though they lack existence, possess being. I develop the notion of possible worlds, in which possible individuals exist, but also point to unsolved problems, such as how to account for the contingency of the actuality of the actual world.

This article starts with an examination of Saul Kripke’s views of the semantics of modal logic and concludes by pointing to some epistemological and ontological consequences of those views that seem to be incompatible with the way empirical science in fact works and progresses. In dealing with the problem of identifying the same objects in different possible worlds, Kripke is led to develop his original positions on topics such as the theses of the fixation of the reference independent of meaning (where he disagrees with Frege) and the noncoincidence between necessary and a priori truths (where he disagrees with Kant). In Kripke’s view, it is a particular type of knowledge – scientific knowledge – that determines what should be considered as essential or necessary. And the statements that represent these a posteriori scientific discoveries “are not,” in his words, “contingent truths, but truths that are necessary in the strictest possible sense.” Thus, in Kripke’s view, our (scientific) knowledge determines without distortion the essential properties of what is real, which turns his ontology into a direct function of the discoveries of empirical science. This “naturalization of ontology”, as shown in the conclusion of this article, is not compatible with recognition of the defeasibility of our semantic or scientific criteria and overloads scientific the endeavor with a metaphysical burden which science itself does not claim and is not capable of carrying. Key words: fixation of reference, a posteriori necessity, naturalized ontology.

In XX century we had a considerable advance on the understanding of the formal meaning of modalities. The Jnsson, McKinsey and Tarski works in fourties enabled the construction of the results of algebraic completeness for the modal systems. In fifties Kripke proposed a interesting semantic for these systems. Such semantics, today known as possible world's semantics, or Kripke's semantics, caused a great impact in the context of analytical philosophy. Articles written by Lemmon in the decade of 60 are supposed to present a synthesis of these two semantics, the algebraic semantic and the possible world's semantic. One interesting result shown in these articles is that the semantic completeness can be inferred from algebraic results through a central theorem. One of the most surprising and interesting results in the paper of Lemmon is the theorem of representation for modal algebras. This theorem of representation for the modal algebra is as a result the connection between the point of view and algebraic point of view of the semantics of possible worlds (or Kripke's semantics). The initial objective of the present work was to extend this same result for algebraic systems of Class G mnpq proposed by Lemmon and Scott in the "Lemmon notes". We argue that the algebraic semantic for modal logic can serve as a basis for answers to the various criticisms directed to the development of modal logic. We'll show, finally, that the algebraic semantics, as a semantics that does not use the concept of possible worlds, may be deemed useful by supporters of modal antirealism.

In this work, we consider a situation when a decision making agent has to choose between a finite set of strategies, having access to the opinions of finite set of autonomous agents. Moreover, the decision making agent is allowed to assign different credibilities to the statements made by the agents. We present this decision situation in terms of Kripke's semantics of possible worlds. The available information is vague and numerically imprecise and the evaluation results in a set of admissible strategies. The concept of admissibility is defined in terms of interval-valued (imprecise) plausibility and belief measures induced by a model of modal logic. The set of admissible strategies is further refined by introducing the notion of reliable agents.

I go through various arguments why the K-principle (aka Distributivity Axiom), O(p→q)→(Op→Oq), a cornerstone of all deontic logic as the latter is standardly conceived, is of little use for the logical analysis of real-life deontic discourse. It is empirically false, I argue. Then I proceed to the question why it is so attractive, and I submit the hypothesis that to blame is Kripke semantics, making use of the imagery of possible worlds, accepted as a de facto standard in deontic logic. This semantics, however, is not attuned to the needs of controlling real-life deontic discourse, as the latter is mostly about things entirely this-worldly. For this-worldly relations possibly founding the deontic modalities the K-principle stands poor chance of working, I argue.

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