Related papers: Syntax and Consequence Relations -- A Categorical …
Semantic theories of natural language associate meanings with utterances by providing meanings for lexical items and rules for determining the meaning of larger units given the meanings of their parts. Meanings are often assumed to combine…
We report on the idea to use colours to distinguish syntax and semantics as an educational tool in logic classes. This distinction gives also reason to reflect on some philosophical issues concerning semantics.
We present the formalization of a theory of syntax with bindings that has been developed and refined over the last decade to support several large formalization efforts. Terms are defined for an arbitrary number of constructors of varying…
We discuss the problem of defining a logic for analogical reasoning, and sketch a solution in the style of the semantics for Counterfactual Conditionals, Preferential Structures, etc.
We introduce A-ranked preferential structures and combine them with an accessibility relation. This framework allows us to formalize contrary to duty obligations. Representation results are proved.
We provide a Lawvere-style definition for partial theories, extending the classical notion of equational theory by allowing partially defined operations. As in the classical case, our definition is syntactic: we use an appropriate class of…
Both syntactic and semantic structures are key linguistic contextual clues, in which parsing the latter has been well shown beneficial from parsing the former. However, few works ever made an attempt to let semantic parsing help syntactic…
Representations are essential to mathematically model phenomena, but there are many options available. While each of those options provides useful properties with which to solve problems related to the phenomena in study, comparing results…
This paper contributes to the mathematical foundations of logic programming by introducing and studying the sequential composition of answer set programs. On the semantic side, we show that the immediate consequence operator of a program…
In this work we suggest the use of a set-theoretical interpretation of semantic tableaux for teaching propositional logic. If the student has previous notions of basic set theory, this approach to semantical tableaux can clarify her the way…
We make explicit the correspondence between syntax and syntactic categories for coherent first-order logic, providing a categorical characterization of bi-interpretability. This is done by creating a biequivalence between a bicategory of…
Starting from a description of various generalized function algebras based on sequence spaces, we develop the general framework for considering linear problems with singular coefficients or non linear problems. Therefore, we prove…
We obtain, for the first time, a modular many-valued semantics for combined logics, which is built directly from many-valued semantics for the logics being combined, by means of suitable universal operations over partial non-deterministic…
Bialgebrae provide an abstract framework encompassing the semantics of different kinds of computational models. In this paper we propose a bialgebraic approach to the semantics of logic programming. Our methodology is to study logic…
A prototypical example of categorial grammars are those based on Lambek calculus, i.e. noncommutative intuitionistic linear logic. However, it has been noted that purely noncommutative operations are often not sufficient for modeling even…
Algebraic theories with dependency between sorts form the structural core of Martin-L\"of type theory and similar systems. Their denotational semantics are typically studied using categorical techniques; many different categorical…
Real-valued logics underlie an increasing number of neuro-symbolic approaches, though typically their logical inference capabilities are characterized only qualitatively. We provide foundations for establishing the correctness and power of…
Traditional treatments of formal logic provide: 1. A syntax for formulas. 2. An inference relation between sets of formulas. 3. A rule for assigning meaning to formulas (semantics) that is sound with respect to the inference relation. First…
This extended abstract gives a brief outline of the connections between the descriptions and variable concepts. Thus, the notion of a concept is extended to include both the syntax and semantics features. The evaluation map in use is…
A type theory is presented that combines (intuitionistic) linear types with type dependency, thus properly generalising both intuitionistic dependent type theory and full linear logic. A syntax and complete categorical semantics are…