Logics doi: 10.3390/logics1020005

Authors: Răzvan Diaconescu

The extension of the (ordinary) institution theory of Goguen and Burstall, known as the theory of stratified institutions, is a general axiomatic approach to model theories where the satisfaction is parameterized by states of models. Stratified institutions cover a uniformly wide range of applications from various Kripke semantics to various automata theories and even model theories with partial signature morphisms. In this paper, we introduce two natural concepts of logical interpolation at the abstract level of stratified institutions and we provide some sufficient technical conditions in order to establish a causality relationship between them. In essence, these conditions amount to the existence of nominals structures, which are considered fully and abstractly.

]]>Logics doi: 10.3390/logics1010004

Authors: Wesley H. Holliday

We give a proof-theoretic as well as a semantic characterization of a logic in the signature with conjunction, disjunction, negation, and the universal and existential quantifiers that we suggest has a certain fundamental status. We present a Fitch-style natural deduction system for the logic that contains only the introduction and elimination rules for the logical constants. From this starting point, if one adds the rule that Fitch called Reiteration, one obtains a proof system for intuitionistic logic in the given signature; if instead of adding Reiteration, one adds the rule of Reductio ad Absurdum, one obtains a proof system for orthologic; by adding both Reiteration and Reductio, one obtains a proof system for classical logic. Arguably neither Reiteration nor Reductio is as intimately related to the meaning of the connectives as the introduction and elimination rules are, so the base logic we identify serves as a more fundamental starting point and common ground between proponents of intuitionistic logic, orthologic, and classical logic. The algebraic semantics for the logic we motivate proof-theoretically is based on bounded lattices equipped with what has been called a weak pseudocomplementation. We show that such lattice expansions are representable using a set together with a reflexive binary relation satisfying a simple first-order condition, which yields an elegant relational semantics for the logic. This builds on our previous study of representations of lattices with negations, which we extend and specialize for several types of negation in addition to weak pseudocomplementation. Finally, we discuss ways of extending these representations to lattices with a conditional or implication operation.

]]>Logics doi: 10.3390/logics1010003

Authors: Valentin Goranko

This paper is an overview of some recent and ongoing developments of formal logical systems designed for reasoning about systems of rational agents who act in pursuit of their individual and collective goals, explicitly specified in the language as arguments of the strategic operators, in a socially interactive context of collective objectives and attitudes which guide and constrain the agents&rsquo; behavior.

]]>Logics doi: 10.3390/logics1010002

Authors: Valentin Goranko

Reasoning is one of the most important and distinguished human activities [...]

]]>Logics doi: 10.3390/logics1010001

Authors: Constanze Schelhorn

Logic (from ancient Greek &ldquo;&lambda;&omicron;&gamma;&iota;&kappa;&#8052; &tau;&#941;&chi;&nu;&eta; (logik&eacute; t&eacute;chn&#275;)&rdquo;&mdash;&ldquo;thinking art&rdquo;, &ldquo;procedure&rdquo;) is a multidisciplinary field of research studying the formal principles of reasoning [...]

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