We study three kinds of compactness in some variants of G"{o}del logic: compactness,entailment compactness, and approximate entailment compactness.For countable first-order underlying language we use the Henkinconstruction to prove the compactness property of extensions offirst-order g logic enriched by nullary connective or the Baaz'sprojection connective. In the case of uncountable first-orde...

Linear Temporal Logic (LTL) is the standard specification language for reactive systems and successfully applied in industrial settings. However, many shortcomings of LTL have been identified, including limited expressiveness, lack quantitative features, inability to express robustness. While there work on overcoming these shortcomings, each typically addressed isolation, which insufficient any...

Annotated Logic was introduced in Sub87] as a logic programming language to implement reasoning with uncertainty for knowledge-based systems. Later, it was shown to be adequate to formalise systems in which inconsistencies can be present, without trivialising its reasoning (technically coined \paraconsistent sys-tems" Cos63]). This Logic was generalised in BS88], but its foundational aspects we...

A strong (L) logic programming language ([14, 15]) is given by two subclasses of formulas (programs and goals) of the underlying logic L, provided that: firstly, any program P (viewed as a L-theory) has a canonical model MP which is initial in the category of all its L-models; secondly, the L-satisfaction of a goal G in MP is equivalent to the L-derivability of G from P , and finally, there exi...

Syllogism reasoning is a common and important form of in human thinking from Aristotle onwards. To overcome the shortcomings previous studies, this article makes full use set theory classical propositional logic, deduces remaining 23 valid syllogisms only on basis syllogism EIO-2 perspective mathematical structuralism, then successfully establishes concise formal axiom system for categorical sy...

We show that the loosely guarded and packed fragments of first-order logic have the finite model property. We use a construction of Herwig. We point out some consequences in temporal predicate logic and algebraic logic. AMS classification: Primary 03B20; Secondary 03B45, 03C07, 03C13, 03C30, 03G15

urban design problems have become so complex that no single designer is able to consider all aspects of a design area simultaneously. lately the application of computerized and scientific methods have helped designers analyze complex problems. one of these new methods is space syntax. the purpose of this study is to first investigate the strengths and weaknesses of this method and then suggest ...

For every finite n ≥ 4 there is a logically valid sentence φn with the following properties: φn contains only 3 variables (each of which occurs many times); φn contains exactly one nonlogical binary relation symbol (no function symbols, no constants, and no equality symbol); φn has a proof in first-order logic with equality that contains exactly n variables, but no proof containing only n − 1 v...