Characterizations and Classifications of Argumentative Entailments

In this paper we provide a detailed analysis of the inference process induced by logical argumentation frameworks. The frameworks may be defined with respect to any propositional language and logic, different arguments that represent deductions in the logic, various support-based attack relations between arguments, and all the complete Dung-style semantics for the frameworks. We show that, ultimately, for characterizing the inference process with respect to a given framework, extension-based semantics may be divided into two types: single-extension and multiple-extension, which induce respective kinds of entailment relations. These entailments are further classified by the way they tolerate new information (nonmonotonicity-related properties) and maintain conflicts among arguments (inconsistency-related properties).

On the structure of early language

Both linguistic and neuroanatomical evidence suggests that there are two modes of processing in linguistic discourse, namely an analytic mode and a holistic mode. Competent speakers of a language know many linguistic entities in two ways: holistically and analytically, and can move between the two. The analytic mode is concerned with propositional language processing based on the compositional format of sentences, clauses, and phrases and their hierarchical organization, while the holistic mode surfaces mainly in unanalyzable, formulaic expressions, for example, in speech act formulas such as interjections (wow, ouch), ideophones (bang, splish-splash), formulae of social exchange (hello, sorry, goodbye). Research on the reconstruction of earlier stages of language evolution has for the most part been restricted to the analytic mode, and grammaticalization theory played an important role in this research. The present chapter demonstrates that a complementary analysis of holistic ways of processing can contribute to a more comprehensive understanding of how human languages may have evolved.

VOLUNTARY IMAGINATION: A FINE-GRAINED ANALYSIS

We study imagination as reality-oriented mental simulation (ROMS): the activity of simulating nonactual scenarios in one’s mind, to investigate what would happen if they were realized. Three connected questions concerning ROMS are: What is the logic, if there is one, of such an activity? How can we gain new knowledge via it? What is voluntary in it and what is not? We address them by building a list of core features of imagination as ROMS, drawing on research in cognitive psychology and the philosophy of mind. We then provide a logic of imagination as ROMS which models such features, combining techniques from epistemic logic, action logic, and subject matter semantics. Our logic comprises a modal propositional language with non-monotonic imagination operators, a formal semantics, and an axiomatization.

AGGREGATION OF SYMBOLIC POSSIBILISTIC KNOWLEDGE BASES FROM THE POSTULATE POINT OF VIEW

Aggregation of knowledge bases in the propositional language was soon investigated and the requirements of aggregation processes of propositional knowledge bases basically are unified within the community of researchers and applicants. Aggregation of standard possibilistic knowledge bases where the weight of propositional formulas being numeric has also been investigated and applied in building the intelligent systems, in multi-criterion decision-making processes as well as in decision-making processes implemented by many people. Symbolic possibilistic logic (SPL for short) where the weight of the propositional formulas is symbols was proposed, and recently it was proven that SPL is soundness and completeness. In order to apply SPL in building intelligent systems as well as in decision-making processes, it is necessary to solve the problem of aggregation of symbolic possibilistic knowledge bases (SPK bases for short). This problem has not been researched so far.The purpose of this paper is to investigate aggregation processes of SPK bases from the postulate point of view in propositional language. These processes are implemented via impossibility distributions defined from SPK bases. Characteristics of merging operators, including hierarchical merging operators, of symbolic impossibility distributions (SIDs for short) from the postulate point of view will be shown in the paper.

AGGREGATION OF SYMBOLIC POSSIBILISTIC KNOWLEDGE BASES FROM THE POSTULATE POINT OF VIEW

Aggregation of knowledge bases in the propositional language was soon investigated and the requirements of aggregation processes of propositional knowledge bases basically are unified within the community of researchers and applicants. Aggregation of standard possibilistic knowledge bases where the weight of propositional formulas being numeric has also been investigated and applied in building the intelligent systems, in multi-criterion decision-making processes as well as in decision-making processes implemented by many people. Symbolic possibilistic logic (SPL for short) where the weight of the propositional formulas is symbols was proposed, and recently it was proven that SPL is soundness and completeness. In order to apply SPL in building intelligent systems as well as in decision-making processes, it is necessary to solve the problem of aggregation of symbolic possibilistic knowledge bases (SPK bases for short). This problem has not been researched so far.The purpose of this paper is to investigate aggregation processes of SPK bases from the postulate point of view in propositional language. These processes are implemented via impossibility distributions defined from SPK bases. Characteristics of merging operators, including hierarchical merging operators, of symbolic impossibility distributions (SIDs for short) from the postulate point of view will be shown in the paper.

Categorical Interpretation of Modal Structures under Bisimulation

In this work we summarise the concept of bisimulation, widely used both in computational sciences and in modal logic, that characterises modal structures with the same behaviour in terms of accessibility relations. Then, we offer a sketch of categorical interpretation of bisimulation between modal structures, which comprise both the structure and the valuation from a propositional language.

Idea Formulation for Spoken Language Production: The Interface of Cognition and Language

Background:Language and communication are fundamental to the human experience, and, traditionally, spoken language is studied as an isolated skill. However, before propositional language (i.e., spontaneous, voluntary, novel speech) can be produced, propositional content or ‘ideas’ must be formulated.Objective:This review highlights the role of broader cognitive processes, particularly ‘executive attention’, in the formulation of propositional content (i.e., ‘ideas’) for propositional language production.Conclusions:Several key lines of evidence converge to suggest that the formulation of ideas for propositional language production draws on executive attentional processes. Larger-scale clinical research has demonstrated a link between attentional processes and language, while detailed case studies of neurological patients have elucidated specific idea formulation mechanisms relating to the generation, selection and sequencing of ideas for expression. Furthermore, executive attentional processes have been implicated in the generation of ideas for propositional language production. Finally, neuroimaging studies suggest that a widely distributed network of brain regions, including parts of the prefrontal and parietal cortices, supports propositional language production.Implications:Theoretically driven experimental research studies investigating mechanisms involved in the formulation of ideas are lacking. We suggest that novel experimental approaches are needed to define the contribution of executive attentional processes to idea formulation, from which comprehensive models of spoken language production can be developed. Clinically, propositional language impairments should be considered in the context of broader executive attentional deficits.

Gentzen sequent calculi for some intuitionistic modal logics

Intuitionistic modal logics are extensions of intuitionistic propositional logic with modal axioms. We treat with two modal languages ${\mathscr{L}}_\Diamond $ and $\mathscr{L}_{\Diamond ,\Box }$ which extend the intuitionistic propositional language with $\Diamond $ and $\Diamond ,\Box $, respectively. Gentzen sequent calculi are established for several intuitionistic modal logics. In particular, we introduce a Gentzen sequent calculus for the well-known intuitionistic modal logic $\textsf{MIPC}$. These sequent calculi admit cut elimination and subformula property. They are decidable.